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High Speed Homodyne Detector for Gaussian-Modulated
Coherent-State Quantum Key Distribution
by
Yuemeng Chi
A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science
Graduate Department of Electrical and Computer EngineeringUniversity of Toronto
5.14 Quadrature value of nth pulse X�n� and that of n+1 pulse Y �n� =X�n+1�at an LO power of 0.77 mW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.15 Key rate simulation as a function of the transmission distance with a
high-speed HD (running at 10 MHz repetition rate) and a low-speed HD
57], however, none is demonstrated at 1550 nm wavelength. High-speed HDs operating
in the telecommunication wavelength region that can be used in quantum optics and
quantum information are still lacking. In this thesis, my goal is to develop a high speed
HD in the telecommunication wavelength that will be suitable for high speed GMCS
QKD experiments.
1.3 Objective
The long term objective is to experimentally develop a high speed QKD system based on
GMCS protocol. This will be achieved by developing high speed modulations, detections,
data acquisitions, classical data processing algorithms, etc (to be discussed in Section
2.1.2). As the first stage to achieve this objective, the goal of my thesis is to enable a
fully-fiber based high speed GMCS QKD system by constructing a fast detection system:
homodyne detector (HD) in the telecommunication wavelength region.
My research is carried out with the following objectives.
• Establish the requirements and challenges of an HD for a high-speed GMCS QKD
system.
• Provide both electrical and optical designs of a high speed HD to meet those re-
quirements.
• Construct and test the HD, and outperform the previous demonstrations reported
in the literature.
Chapter 1. Introduction 8
• Evaluate HD performance in real QKD and suggest directions for future high speed
GMCS QKD experimental implementation.
1.4 Organization
The thesis is organized as follows: I briefly review the development of GMCS QKD and
homodyne detection in Chapter 2, from principle to the state of the art. In Chapter 3,
I will discuss an example of using a custom-designed low speed HD in a 20-km GMCS
QKD implementation over an existing system. The main work of this thesis is discussed
in Chapter 4 and Chapter 5. In Chapter 4, requirements of a high speed HD that can
be used in high speed GMCS QKD experiments are presented. Challenges and solutions
of constructing a high speed HD are also discussed in this chapter. In Chapter 5, I will
present the testing results of our constructed HD in both time and frequency domains,
with CW and pulsed light, respectively. Our results show that this HD has a bandwidth
of � 100 MHz, which will enable GMCS QKD experiments at a repetition rate of 10
MHz. The expected key rate of GMCS QKD experiments with this HD will be increased
by 1-2 orders of magnitude, which is comparable to the high speed QKD based on single
photon protocols. In Chapter 6, I will summarize the thesis, discuss the significance of
the work and suggest future work for developing a high speed GMCS QKD system.
Chapter 2
Review of GMCS QKD and
Homodyne Detection
2.1 Gaussian-modulated coherent-state quantum key
distribution
Over the past few years, quantum key distribution (QKD) using Gaussian-modulated
coherent-state (GMCS) protocol has drawn a lot of attention [19, 39, 40, 41, 42]. The
uncertainty principe, which states that the amplitude quadrature (x) and the phase
quadrature (p) of a coherent state cannot be precisely known simultaneously, is the foun-
dation of GMCS QKD. Any eavesdropping of one quadrature will introduce additional
noise to the other quadrature. Alice and Bob are able to detect Eve if they monitor the
variances of x and p together. In this section, I will give an overview of the GMCS QKD
protocol and the state of the art of this topic.
2.1.1 Protocol
In the classical electromagnetism, a light field can be characterized by x cosωt + p sinωt,
where ω is the angular frequency, and x and p are amplitude and phase quadratures.
9
Chapter 2. Review of GMCS QKD and Homodyne Detection 10
When the light intensity is very weak and the quantum effect is considered, the measure-
ment of one quadrature will introduce more uncertainty to the other quadrature. In the
GMCS QKD, Alice encodes x and p on each bit and Bob randomly chooses x or p to
decode information. Eve does not know which basis Bob will select to perform measure-
ment. If Eve eavesdrops in a random basis, according to the uncertainty principle, her
measurement of x (p) will disturb the variable p (x), i.e. Eve cannot simultaneously re-
duce measurement error on both quadratures. Therefore, the presence of Eve inevitably
introduces additional noise in Bob’s measurements, which we call excess noise. After the
key transmission, by comparing some of Bob’s measurement results with the x, p values
prepared by Alice, Bob can estimate the excess noise, which is attributed to Eve. Hence,
Bob can estimate the amount of information leaked to Eve. Alice and Bob then distill
the secure information by a classical data processing. Note that, the difference between
GMCS QKD and classical optical communication is that weak (quantum) signal is used
in GMCS QKD. If the excess noise in GMCS QKD is above a threshold, no secure key
can be transmitted. An example of using a strong signal in GMCS QKD will be shown
in Fig. 3.4 of Section 3.3, in which no positive secure key is generated.
The protocol of the GMCS QKD is described as follows (shown in Fig. 2.1) [19, 43,
39, 45, 58].
1. Alice generates two random sets of continuous variables x and p with a Gaussian
distribution that has a zero average (variance = VAN0, N0 is the shot noise unit).
For a continuous Gaussian noise channel, a Gaussian distribution of the input will
yield an optimal channel capacity [59]. In the GMCS QKD, Alice encodes random
bits (key information) by modulating the amplitude quadrature (x) and the phase
quadrature (p) of weak coherent states �x + ip� (typically less than 100 photons
in each pulse) with her Gaussian distributed sets x, p. Experimentally this is
realized by modulating the intensity and the phase of each pulse. On the receiver’s
side, Bob measures either x or p quadrature of the weak coherent states randomly
Chapter 2. Review of GMCS QKD and Homodyne Detection 11
Figure 2.1: GMCS QKD protocol.
by using a homodyne detection. Note that, the signal cannot be amplified before
being detected, since quantum coherent states cannot be perfectly cloned without
paying penalty (adding excess noise).
2. Through an authenticated public channel (Eve can listen to the information but
cannot modify), Bob informs Alice about the quadratures he picked. Alice then
discards the quadratures that were not measured by Bob. At this stage, Alice
shares a set of correlated Gaussian variables (called the ”raw key”) with Bob.
3. Alice and Bob then publicly compare a random sample of their raw key to evaluate
the transmission efficiency of the quantum channel ηG (including channel efficiency
G and Bob’s system efficiency η), and the excess noise ε of the QKD system. Excess
noise is the noise above the vacuum noise level associated with channel losses [39].
It reflects possible leakage information to Eve. Based on the parameters, Alice and
Bob can evaluate their mutual information IAB and the information obtained by
Eve IBE1[19, 60]. This stage is a classical data processing process and can be
1Here, we assume the secure key is made of Bob’s data. Bob will publish some of his measurements
Chapter 2. Review of GMCS QKD and Homodyne Detection 12
divided into reconciliation (correcting the errors while minimizing the information
revealed to Eve. In this thesis, we only consider reverse reconciliation) and privacy
amplification (making the key secret). If the reconciliation is perfect, a secure key
of length IAB − IBE will be distilled after the classical data processing.
2.1.2 State of the art
The GMCS QKD protocol was developed in 2002 [28]. The security of the GMCS QKD
was first proven against individual attacks with direct [28] or reverse [19, 60] reconciliation
schemes. Security proofs were then given against general individual attacks [60] and
general collective attacks [43, 61, 62]. Until recently, three groups have independently
claimed they proved the unconditional security [63, 64, 65].
The first GMCS QKD experiment based on homodyne detection was demonstrated
in free space [19]. This experiment was carried out with 780 nm optical light. Hence
it did not establish the feasibility of implementation in fiber communication networks,
which are widely used for long-distance communication.
Fiber-based GMCS QKD systems over a practical distance remain challenging. So
far only two groups have implementations of the GMCS QKD over a practical distance
operated fully on fiber-based components [1, 43, 66]. To reduce excess noise arising from
the leakage from the local oscillator (LO), in Ref. [43], Mach-Zehnder interferometers
(MZIs) with largely imbalanced path lengths (80 m) were employed to separate the signal
and the leakage in the time domain (time-multiplexing scheme). However, in practice it
is quite challenging to stabilize a MZI with a large length imbalance.
One recent paper [66] by the same group reported a field test of a GMCS QKD
prototype integrated into a preinstalled quantum cryptography telecommunication net-
work. In that paper, a polarization-time multiplexing scheme is employed. The system
and Alice will modify her data according to Bob’s results. This process is called reverse reconciliationsince this flow has a reverse direction from the key transmitting flow.
Chapter 2. Review of GMCS QKD and Homodyne Detection 13
is running at 500 kHz laser repetition rate.
In contrast, our group (Experimentalists: Dr. Bing Qi and Lei-Lei Huang, under the
supervision of Profs Li Qian and Hoi-Kwong Lo) has developed a polarization-frequency-
multiplexing scheme to effectively suppress the leakage of the LO with balanced MZIs.
[1]. The system design will be described in Section 3.1. In this experiment, the laser
repetition rate is 100 kHz.
In parallel with GMCS QKD based on homodyne detection, a heterodyne detection
scheme, in which Bob measures both x and p quadratures simultaneously, was proposed
[67] (Note that, local oscillator and signal are at the same frequency. The heterodyne
detection used here is different from that defined in classical communication in which
local oscillator and signal are at different frequencies). The security proof of the GMCS
QKD based on heterodyne detection is given in Refs. [63, 68]. With this scheme, there is
no need to choose a random quadrature on Bob’s side. The experimental implementation
of GMCS QKD based on heterodyne detection has been realized in 2005 [69].
Although the GMCS QKD has a potential application in transmitting at high key
rates, so far all reported experimental systems are running below 1 MHz. There are
several limitations for a practical GMCS QKD system in achieving high speeds.
• The repetition rate of a GMCS QKD system is essentially limited by the homodyne
detector (HD) bandwidth. In QKD, each pulse quadrature encoded with Gaussian
random numbers has to be measured individually in the time domain. This will
require the response time for HD to be shorter than the inverse of the laser repeti-
tion rate. In other words, the bandwidth of the HD in the frequency domain should
be greater than the repetition rate. Intuitively, one should increase the bandwidth
of the HD to obtain a high repetition rate. However, the electronic noise is pro-
portional to the HD bandwidth [1, 40]. A wider bandwidth will result in greater
electronic noise and lead to a lower secure key rate [1].
Chapter 2. Review of GMCS QKD and Homodyne Detection 14
• The repetition rate is also limited by the speeds of computer-driven data acquisition
systems, which are typically lower than a few MHz. In Ref. [1] , a data acquisition
card (NI, PCI-6115) with a sampling rate of 10 M samples/s is employed to acquire
data. If one wants to get sufficient data points for each pulse (like 20), the maximum
repetition rate can only be a few hundreds of kHz.
• Speed of the classical reconciliation data processing will limit the GMCS QKD
speed.
Owing to the above limitations, there is no reported GMCS QKD experiment above
1 MHz repetition rate. For a GMCS QKD key transmission demonstration, if data
processing is not performed in the real time, a fast oscilloscope (40 G Samples/s) can be
used to acquire and store raw data. Considering that the HD bandwidth is a fundamental
limitation, we will develop a fast HD that can enable a high speed GMCS QKD system
in this thesis.
2.2 Homodyne detection
2.2.1 Introduction
Homodyne detection is a well-established technique for measuring the amplitude and
phase quadrature of a weak optical signal [49, 70]. Fig. 2.2 shows a schematic of homo-
dyne detection. The signal is mixed at a beam splitter (with a 50/50 splitting ratio) with
a strong local oscillator (LO)[49, 71, 72] with a defined optical phase (φ in Fig. 2.2).
This phase is introduced by a phase modulator at the LO beam in Fig. 2.2. The output
ports of the beam splitter are attached to two photodiodes. The photocurrent difference
(after the subtraction shown in Fig. 2.2) is finally amplified by an electronic amplifier.
I follow Ref. [72] to derive the output of a homodyne detection. The electric fields of
the signal ES�t� and the LO EL�t� are
Chapter 2. Review of GMCS QKD and Homodyne Detection 15
Figure 2.2: Schematic of a homodyne detection. BS: beam splitter; SIG: signal; LO:
local oscillator; PD: photodiode; φ: introducing a phase between the signal and the LO;
Black line: optical path; Blue line: electrical path; Dashed box: homodyne detector
ES�t� = ES + δXS�t� + iδPS�t�, (2.1)
and
EL�t� = EL + δXL�t� + iδPL�t��eiφ. (2.2)
where ES and EL are real time-independent terms, δXS�t� and δPS�t� (δXL�t� and
δPL�t� ) 2 are real and describe changes of amplitude and phase quadratures of the
signal (LO) field. Re ES�t�� = ES + δXS�t� is the amplitude quadrature of the signal,
while Im ES�t�� = δPS�t� is the phase quadrature of the signal. Here the spatial mode
distribution and the fast oscillating term eiωt are neglected. Fig. 2.3 shows signal and
LO states in the phasor space.φ in Fig. 2.3(same as φ in Fig. 2.2) is the relative phase
difference between the signal and the LO. For the case where the LO beam is far more
intense than the signal beam EL � ES [71, 72], the electric fields after the beam splitter
2Here, I use upper cases X and P to represent electric field quadratures, in order to distinguish withthe Gaussian distributed quadratures �x, p� used in QKD.
Chapter 2. Review of GMCS QKD and Homodyne Detection 16
Figure 2.3: LO and signal states in the phasor space.
E1�t� and E2�t� are,
E1 = 1�2�EL +ES�, (2.3)
and
E2 = 1�2�EL −ES�. (2.4)
The photocurrents from the two photodiodes are proportional to �E1�2 and �E2�2 re-
noise) + Nleak (leakage noise). Under this model, Eve has no control over Bob’s devices.
1. εA is the excess noise due to imperfections outside Bob’s system, which includes
the phase noise of the laser source, imperfect amplitude and phase modulations,
the phase noise of the interferometers, etc.
Chapter 3. GMCS QKD over 20 km Fiber 28
Figure 3.3: QKD experimental results. The equivalent input noise has been determined
experimentally to be χ = 6.13[6, 7].
Following [39], we assume that εA is proportional to the modulation variance VA
and can be described by εA = VAδ. To estimate the value of the coefficient δ,
Alice uses a large modulation variance (VA � 40000) to encode her information and
employs a weak LO (105 photon/pulse, to reduce the leakage). With the same
process as QKD, the equivalent input noise χ and excess noise ε can be achieved
from the experimental results. Assuming all other excess noise in Eq. (3.2) except
εA are negligible, i. e. χ � VAδ 1, δ can be determined from experimental results
of the equivalent input noise χ and the modulation variance VA. Note that, large
modulation is not used for real QKD since excess noise is so strong that no secure
key can be distributed between Alice and Bob.
Figure 3.4 shows the correlated variables of Alice and Bob when a large modulation
1χ in Fig. 3.4 (with a large modulation VA) is 32 times larger than that of Fig. 3.3 (in real QKDwhen weak signal is used)
Chapter 3. GMCS QKD over 20 km Fiber 29
Figure 3.4: Determine δ by using a high modulation variance VA � 40000 and a weak LO
(105 photon/pulse). The result is δ = 0.0049
VA is used. The calculated δ is = 0.0049. Therefore, for a modulation variance of
VA = 10, the expected excess noise outside Bob’s system is εA = δVA =0.049.
2. From Eq. (3.2) and the estimated εA above, the noise from Bob’s sytem NBob is
0.26.
There are two main sources of NBob, the electronic noise from the HD (Nele) and
the noise associated with the leakage from LO to signal (Nleak).
(a) As shown in Fig. 3.5, the total noise of HD (variance of HD output voltages)
is related to the LO power by a form of y = ax + b (y: total noise of the
HD, x: LO power, a, b are constants) when vacuum state is detected (i. e.
vacuum is sent to HD signal port). This test is extremely important since it
verifies the HD noise is indeed the sum of the shot noise and electronic noise.
The HD has a 6.8 dB shot-noise-to-electronic-noise ratio when the QKD is
Chapter 3. GMCS QKD over 20 km Fiber 30
Figure 3.5: Noise of the balanced HD as a function of LO power. With a LO of 1.2�107
photons/pulse, the electronic noise is 6.8 dB below the shot noise (plot with raw data
obtained from [1])
performed at an LO of 1.2 �107 photons/pulse. The corresponding Nele is
therefore 10−0.68 = 0.21 (in shot noise unit).
According to above noise analysis, the electronic noise of the HD will con-
tribute to the excess noise and ultimately affect the secure key rate, which
is shown in the key rate simulation in Fig. 3.6 under the “general model”
[19] (based on Eqs. (3.1),(3.3) and (3.4) in Section 2.1.1). Parameters in this
simulation are obtained from Ref. [1] and shown in Table 3.1. As shown in
Fig. 3.6, the key rate drops as the electronic noise increases. Positive secure
key can be achieved as the electronic noise is below 0.13 (in shot noise unit),
i.e. 8.86 shot-noise-to-electronic-noise ratio2. Therefore, we will need a � 10-
2In the “general model”, electronic noise from Bob’s homodyne detector can be controlled by Eve.Under the “realistic model”, we are able to tolerate a stronger electronic noise if we assume Eve has nocontrol over Bob’s system.
Chapter 3. GMCS QKD over 20 km Fiber 31
0 0.02 0.04 0.06 0.08 0.1 0.12 0.140
0.05
0.1
0.15
0.2
0.25
Electronic noise (in shot noise unit)
Key
rat
e (b
it/p
uls
e)
Figure 3.6: Secure key rate as a function of the electronic noise (in shot noise unit) under
the “general model”. Parameters in this simulation are in Table 3.1 .
times shot-noise limited HD (shot noise is 10 dB above the electronic noise)
in GMCS QKD experiments.
For the particular HD used in the 20-km GMCS QKD experiment, the band-
width is about 1 MHz, which limits the pulse repetition rate at 100 kHz. To
enhance the speed, a broadband HD should be used in the GMCS QKD. How-
ever, the electronic noise scales with the HD bandwidth. A broad bandwidth
will include more electronic noise which also deteriorates QKD key rate by
increasing Nele. Therefore, we have to make a tradeoff between the repetition
rate and the electronic noise.
(b) Noise due to leakage photon from LO to signal is another excess noise source
Table 3.1: Parameters used in the key rate simulation , from Ref. [1]. The length of the
fiber is 5 km.
VA G η εA Nleak β
16.9 0.758 0.44 0.056 0.02 0.898
Chapter 3. GMCS QKD over 20 km Fiber 32
Figure 3.7: The leakage from LO to signal. LO: local oscillator; SIG: signal; LE: leakage;
PBS: polarization beam splitter; LO is 5-6 orders of magnitude higher than signal. The
leakage from signal to LO is negligible. Arrowed lines indicate the polarization of the
beam
in Bob’s system. Nleak can be calculated by subtracting Nele from NBob, i.e.
Nleak = 0.05 (in shot noise unit). As shown in Fig. 3.7, polarization drift of
the signal and the LO before they enter the polarization beam splitter (Fig.
3.7, drifting from states shown in solid lines to states shown in dotted lines)
will induce leakage photons from the LO to the signal beam. These leakage
photons will interfere with LO and contribute to excess noise.
Leakage photon number will be larger at a stronger LO power. To suppress
Nleak, a weak LO power is preferred. However, shot noise is scaled with LO
power and it is the noise unit in our experiment. At a lower LO power, Nele
(in shot noise unit) due to HD electronic noise will become larger. Therefore,
a tradeoff between Nele and Nleak has to be made. In future GMCS QKD ex-
periments, a more systematic investigation on this issue should be performed.
The experimental results are summarized in Table 3.2. Using Eqs. (3.1),(3.4) and
(3.7), the secure key rate is 0.05 bit/pulse 3 (β= 0.898) over 20 km fiber under the
“realistic model”.
3.4 Discussions
Table 3.3 compares our key rate with that of Ref. [4] based on decoy BB84 protocol.
Both systems are implemented over 20 km telecom fiber.
Table 3.3: Secure key rate in our GMCS QKD experiment and in Ref. [4] over 20-km
fiber. rep. :repetition
Our experiment Ref. [4]
Key rate (bit/pulse) 0.05 0.00098
Key rate (bit/s) 5 k (100 kHz rep. rate) 1.02 M (1.036 GHz rep. rate)
For the key rate per pulse, our GMCS QKD experiment has an obvious advantage,
because (1) HD with high-efficiency PIN photodiodes (HD efficiency= 72 %) is used in
our experiment while low-efficiency single photon detector (10 %) is used in Ref. [4] ; (2)
more than one bit can be obtained in each pulse based on GMCS protocol. However, the
key rate per second of Ref. [4] is two orders of magnitude higher than that of our GMCS
QKD experiment, due to its fast repetition rate at GHz. Therefore, at a low repetition
rate of 100 kHz in our experiment, the advantage of GMCS QKD cannot be thoroughly
demonstrated.
3The secure key rate is less than 1 bit/pulse. After the key transmission, Alice and Bob will performreverse reconciliation and privacy amplification, which will sacrifice a lot of bits.
Chapter 3. GMCS QKD over 20 km Fiber 34
To increase the secure key rate of the GMCS QKD, the subsequent improvements can
be made in future experiments.
• Implement ultra-low loss fiber
Key rate is a function of the channel transmittance G, which is dependent on the
fiber loss. A high transmittance (low loss) channel will yield a high secure key.
Currently ultra-low loss fiber with a loss of 0.164 dB/km has been developed by
Corning and is already used in quantum cryptography experiment [80]. If we use
this ultra-low loss fiber in our GMCS QKD system, we can expect to improve the
secure key rate. Fig. 3.8 shows the secure key rate as a function of the transmission
distance for ultra-low loss fiber and standard fiber (loss 0.21 dB/km) respectively.
Although ultra-low loss fiber can increase the transmission distance by 10 km, the
key rate over a short distance does not improve too much (less than one order).
Furthermore, this ultra-low loss fiber is 3 times more expensive than that of the
standard fiber (based on their quotation).
• Reduce excess noise
In the GMCS QKD, Eve can obtain information by monitoring excess noise. Min-
imizing the excess noise can also improve the secure key rate. However, for a
practical system, the phase noise, polarization noise, electronic noise of Bob’s ho-
modyne detector and losses in Bob’s system will contribute excess noise [39]. To
see the improvement achieved by eliminating the excess noise, key rate is simulated
with excess noise and in the absence of excess noise (although it is hard to realize
in a practical system) in Fig. 3.9. GMCS QKD key rate can not be improved by
orders even though a very unrealistic situation of no excess noise is assumed.
• Increase the bandwidth of our homodyne detector
Although the key rate per pulse of the GMCS QKD is 2 orders of magnitude higher
than that of single photon QKD, the repetition rate at 100 kHz in our experiment
Chapter 3. GMCS QKD over 20 km Fiber 35
0 10 20 30 40 50 60 7010
−6
10−5
10−4
10−3
10−2
10−1
100
Distance (km)
Key
rat
e (b
it/p
uls
e)
Standard fiber
Low loss fiber
Figure 3.8: Key rate simulation when ultra-low loss fiber and standard fiber are used
in the GMCS QKD experiment. Parameters are based on Table 3.2 under the “realistic
model” when β = 0.898
is far lower than that of Ref. [4] at GHz. Thus, GMCS QKD key rate per second
is 2 orders of magnitude lower. If the repetition rate of GMCS QKD experiments
can be successfully increased by 100-1000 times, key rate per second of GMCS
QKD experiments will achieve � Mbits/s, comparable with Ref. [4]. Constructing
a high speed HD is an effective way to improve the secure key rate of GMCS QKD
experiments by a few orders.
3.5 Summary
In summary, as an example of using HD in a real QKD implementation, we demonstrated
a GMCS QKD experiment over 20 km fiber based on our existing system. Under the
Chapter 3. GMCS QKD over 20 km Fiber 36
0 5 10 15 2010
−2
10−1
100
Distance (km)
Key
rat
e (b
it/p
uls
e)
With excess noise
Without excess noise
Figure 3.9: Key rate simulation with excess noise and in the absence of excess noise.
Parameters are based on Table 3.2 under the “realistic model” when β = 0.898
“realistic model” with β = 0.898[19], our key rate over a 20-km fiber is 0.05 bit/pulse.
To greatly enhance the secure key rate in GMCS QKD experiments, several improve-
ments, such as using ultra-low loss fiber, minimizing the excess noise, and increasing the
repetition rate, are discussed. Comparing their predicted improvements, increasing the
repetition rate of GMCS QKD experiments will be the most effective way of enhancing
the key rate by a few orders, which will require a high speed homodyne detector in the
region of telecommunication wavelength. We will discuss our high speed HD construction
and performance in the subsequent two chapters.
Chapter 4
High Speed Homodyne Detector
As discussed in Section 2.1.2, the speed of GMCS QKD is mainly limited by the homodyne
detector (HD) bandwidth. In this chapter, high speed HD requirements will be analyzed.
As the first stage to enable a high speed GMCS QKD system, designs and challenges in
constructing a high speed HD will be discussed from both electrical and optical sides.
Much of the work reported in Chapter 4 and 5 was done by me, under the daily
supervision of Dr. Bing Qi and in frequent discussions with Profs. Li Qian and Hoi-
Kwong Lo. HD circuit design and printed circuit broad layout are provided by Prof.
Alex Lvovsky’s group at University of Calgary.
4.1 Requirement of a homodyne detector in GMCS
QKD
As discussed in Section 3.3, HD with a high shot-noise-to-electronic-noise ratio is pre-
ferred for the GMCS QKD experiment. Note that, theoretically the shot-noise-to-
electronic-noise ratio can always be improved by increasing the LO power. However, for a
practical HD, the photodiodes and electronic amplifier will be saturated if the LO power
is sufficiently high (� 109 LO photon/pulse reported by [5, 43]). Hence our proposed goal
37
Chapter 4. High Speed Homodyne Detector 38
is to construct a 10-times shot-noise limited HD (with a shot-noise-to-electronic-noise
ratio of 10 dB) at an LO of 108 − 109 photons/pulse.
The repetition rate of the GMCS QKD experiment described in Chapter 3 is at 100
kHz, which is fundamentally limited by the HD bandwidth. Considering that extending
the bandwidth of the HDs to � 100 MHz is feasible (demonstrated by [47], but not in
the telecommunication wavelength), my goal is to construct an HD with a bandwidth of
�100 MHz, which can improve the speed of GMCS QKD experiments by � 100 times.
4.2 High speed homodyne detector design
A full homodyne detection system includes both optical and electrical designs (see Fig.
2.2 in Chapter 2). On the optical side, the LO and the signal mix at the beam splitter and
the two output beams need to be carefully balanced before being sent to photodiodes.
On the electrical side, HD circuit will perform a subtraction of the two electrical signals
generated by photodiodes and amplify this differential signal. In this section, a particular
homodyne detection design used in the telecommunication wavelength region will be
presented.
4.2.1 Homodyne detector optical setup in fiber
Based on telecommunication components, the optical setup of the homodyne detection
can be designed as shown in Fig. 4.1 (left dashed line box) , which is a practical imple-
mentation of Fig. 2.2 at 1550 nm wavelength. In this setup, the signal and the LO beams
with the same frequencies will interfere at a two-by-two fiber coupler (FC in Fig. 4.1)
with a splitting ratio of 50:50. A variable optical attenuator (VOA) and an optical vari-
able delay (OVD) are placed in the output paths of the fiber coupler, for adjusting losses
and the lengths of the two paths accurately. Finally, the balanced signals will be sent
to two photodiodes. To avoid disturbance from the environment, such as atmospheric
Chapter 4. High Speed Homodyne Detector 39
Figure 4.1: Homodyne detection setup in the telecommunication wavelength. LO: local
turbulence, I used an enclosure to isolate the system of Fig.4.1.
4.2.2 Homodyne detector electrical circuit
The HD circuit design and the printed circuit board layout we use are from Prof. Alex
Lvovsky’s group at the University of Calgary. They have demonstrated quantum tomog-
raphy experiments in characterizing the coherent or squeezed states at 800 nm wavelength
[56, 81]. Although in this thesis we are primarily interested in the telecommunication
wavelength region (rather than 800 nm), their circuit design should be useful, because
after the conversion of optical signals to photocurrents by the photodiodes, the subse-
quent amplification will not be dependent on the wavelength. In practice, HD circuits
with photodiodes working in the telecommunication wavelength region have to be tuned
carefully to obtain an optimal condition for high speed GMCS QKD experiment, which
we shall discuss in Section 4.3.
Table 4.1: Specifications of FGA04 InGaAs photodiode (typical values).
Bandwidth Responsivity Capacitance Noise equivalent power Dark current
(GHz) (A/W) (pF) (W/�
Hz) (nA)
2 0.9 1.0 1.5�10−15 0.5
Chapter 4. High Speed Homodyne Detector 40
Figure 4.2: A simplified homodyne detector circuit. PD: photodiode (Thorlabs,FGA04);
OPA847: operational amplifier (Texas Instrument)
A simplified HD circuit (illustrated by the right dashed line box in Fig. 4.1) is shown
in Fig. 4.2. Owing to high responsivity and high speed, two InGaAs photodiodes from
Thorlabs (FGA04) are employed in the HD circuit. Table 4.1 shows their specifications.
The two photodiodes are reversely biased and followed by two OPA847 operational am-
plifiers. All components are soldered on a printed circuit board, which is eventually
shielded by a custom-designed metal box.
Given the optical and the electrical designs of a high speed HD, we will discuss the
construction challenges in the next section.
4.3 Challenges
Constructing a broadband HD used for quantum detection is quite challenging and only
a few groups in the world have successfully demonstrated HDs with 100 MHz bandwidth
[5,30 - 32]. In this section, I will discuss those challenges and our corresponding solutions.
Chapter 4. High Speed Homodyne Detector 41
4.3.1 Low electronic noise
As discussed in Section 3.3, a high shot-noise-to-electronic-noise ratio of an HD at a
particular LO power will correspond to a low electronic noise and yield a high secure key
rate, hence, an HD with ultra-low electronic noise is desired in GMCS QKD experiments.
In a practical HD circuit, there are several sources that will contribute to electronic
noise [72],
1. Dark noise of photodiodes, which is only the noise due to photodiode dark current.
2. Johnson noise (thermal noise) of circuit. It is given by 4kBTBR , where kB is the
Boltzmann constant, T is temperature, B is bandwidth and R is the impedance of
the circuit.
3. Electronic amplifier noise. It is in the form of 2eGBF , where e is the elementary
charge, G is the voltage gain, B is the bandwidth and F is called excess noise factor
(Note that, the excess noise is different from that in GMCS QKD).
Compared to Johnson noise and electronic amplifier noise, photodiode dark noise is
usually neglected [72]. Since the gain for a HD is huge, the electronic amplifier noise is
� 7 orders of magnitude higher than that of Johnson noise 1. Therefore, most of the HD
electronic noise is contributed by electronic amplifier noise.
The HD circuit is built on a printed circuit board with discrete surface mounted
components (shown in Fig. 4.3). The two photodiodes are placed closely in the upper
left corner of the board. To minimize the parasitic capacitance, pins of the photodiodes
are cut as short as possible and mounted very close to the board.
Shielding of electromagnetic waves is also very important in reducing the impact of the
environmental noise on the circuit [83]. In discussion with engineers from 3GMetalWorx
1If T = 300 K, R = 50 Ohm, G = 2200 (see Section 4.3.3, we have converted the trans-impedancegain into voltage gain), and F is of the order of 1 [82], the ratio of Johnson noise to electronic amplifiernoise is � 10−7.
Chapter 4. High Speed Homodyne Detector 42
Figure 4.3: Photo of the circuit board of the homodyne detector. Two FGA04 photodi-
odes are in the upper left corner.
Inc., our group designed a customized metal box to shield HD circuit board, as shown
in Fig. 4.4. In this shielding design, HD power and output are placed in separated
compartments in order to minimize their radiations. On top of the board, separated
metal walls are used to prevent the crosstalk among the photodiodes, the amplifiers and
the output wire. Finally, two covers for the separated walls and the box are implemented
to completely shield the HD detector.
4.3.2 Different photodiode response functions
The HD requires two photodiodes with almost identical response functions, however,
practical fabrication process cannot yield identical photodiodes. Figure 4.5 shows the
impulse response measurement circuit and results for ten photodiodes (see the figure
caption for measurement descriptions). Hence two photodiodes selected for the HD will
inevitably exhibit response mismatch in the time domain, which we call photodiode
mismatch. The residual signal after subtraction and amplification cannot be neglected.
Fig. 4.6 shows the residual signal at the output of HD, after balancing the two optical
signals to the photodiodes.
Chapter 4. High Speed Homodyne Detector 43
Figure 4.4: Customized metal box for shielding, constructed by 3GMetalWorx Inc.. Di-
A strong LO power is preferred to achieve a large shot-noise-to-electronic-noise ratio,
since shot noise scales with the LO power. Owing to the large gain of the HD electronic
amplifiers (� 2.2 � 104 V/A, to be shown in Section 4.3.3), residual signal induced by
photodiode mismatch will exceed HD output saturation level when the LO power is
sufficiently high. However, if a low LO power is chosen to avoid saturation, shot noise may
not be able to exceed electronic noise. Hence, minimizing the residual signal is necessary
in achieving a high shot-noise-to-electronic-noise ratio. In the context of GMCS QKD,
the residual signal should be less than 10−4 of the signal of one arm [39]2.
To overcome this problem, (1) a wide pulse with long rising/falling time is used to
minimize the mismatch, since both positive and negative electrical pulses generated by
photodiodes will be smooth with long rising/falling time. Fig. 4.7 compares the impulse
2This is a rough estimation. Assuming that each arm has 108 photons/pulse, shot noise will be � 104
photon/pulse (square root of the arm signal), due to the photon number poissonian distribution of acoherent pulse. Since we want to observe shot noise without saturating the amplifiers, the residual signalshould not be larger than the shot noise.
Chapter 4. High Speed Homodyne Detector 44
Figure 4.5: Photodiode impulse responses test. (a)Photodiode impulse responses test
(generated by a function generator, repetition rate: 10 MHz; pulse width: 50 ns) is sent
to the circuit in (a). The output is measured by an oscilloscope.
2. Output pulse peak voltage is measured by an oscilloscope at the HD electronic
amplifiers output.
3. Measurements in step 1 and 2 are repeated with different input electrical signals.
Output pulse peak voltage (absolute value) is plotted as a function of the input pulse
peak voltage (absolute value) for both positive and negative signals in Fig.4.9. HD
electronic amplifier gains are almost the same for both positive and negative signals in
the amplifiers linear region (deviating �1 % from the linear fit). According to Fig.4.9,
the voltage gain (slope) is 22. Because the resistor connected to the first amplifier input
in Fig. 4.8 (a) has a 1000 Ohm resistance, the trans-impedance gain of the HD electronic
amplifiers is 2.2 � 104 V/A 4.
4.3.4 Laser source
A pulsed laser source is required in GMCS QKD experiments. Here we will discuss the
choice of the pulse repetition rate and pulse width. The linewidth and phase noise of
4With an input voltage of V , the input current across the 1000 Ohm resistor is V/1000. Since theoutput voltage is 22 V , the trans-impedance gain will be the output voltage divided by the input current22V /(V /1000) = 2.2�104 V/A.
Chapter 4. High Speed Homodyne Detector 48
0 10 20 30 40 50 60 700
200
400
600
800
1000
1200
1400
1600
1800
2000
Input peak voltage (mV)
Ou
tpu
t p
eak
volt
age
(mV
) Positive signal input
Negative signal input
Figure 4.9: Output peak voltage as a function of the input peak voltage for both positive
and negative signals. The slope (HD electronic amplifiers voltage gain) is 22. The straight
line is the linear fit.
the laser source are not considered here since they will contribute to εA of the excess
noise ε. In GMCS QKD, excess noise is assumed to be controlled by Eve and insecure
information can be removed by future classical data processing.
• Pulse repetition rate
Pulse repetition rate is fundamentally limited by the bandwidth of the HD. Com-
mercial photodiode can go up to 100 GHz. However, due to the ultra-low noise
requirement of GMCS QKD experiments, HD amplification circuit has a maximum
bandwidth of 100-250 MHz so far [5, 56], since HD electronic amplifier noise scales
with its bandwidth.
The residual signal due to incomplete subtraction of the positive and negative pho-
tocurrents also limits the repetition rate. As an optical pulse strikes the photodiode,
the photocurrent will be generated. If the incident optical pulse width is too nar-
Chapter 4. High Speed Homodyne Detector 49
row, the photodiode may not be fast enough to respond and significant oscillations
will occur at the falling edge of the electrical pulse. Since two photodiodes are
employed in the HD circuit, in addition to photodiode intrinsic mismatch (such as
responsivity, and response time), different oscillation shapes from the two photodi-
odes will result in a considerable residual signal. Hence, wide optical pulse is used
to minimize the oscillations, however, this will limit the repetition rate.
• Pulse peak power and width
In the GMCS QKD, the photon number in each LO pulse is of the order of 107−109,
to ensure (a) the shot noise exceeds the electronic noise ; (2) the electronic circuit
is not saturated. Here I will discuss photodiode linearities in this required power
range.
The circuit and the setup shown in Fig. 4.10 are used in this test. Two types of
pulsed laser sources (shown in Table 4.2) running at 10 MHz repetition rate are
used to test photodiode linearity.
The experimental procedure is:
1. I send pulsed light (laser I or laser II) to only one photodiode by connecting
the switch with port 1 in Fig. 4.10 (b) and use an oscilloscope to measure
the electrical pulse peak voltage across the 10 Ohm resistor in Fig. 4.10 (a).
Optical power of the pulsed light is measured by connecting the switch with
port 3 in Fig. 4.10 (b).
2. Step 1 is repeated by sending pulsed light to the other photodiode when the
Table 4.2: Specifications of the two lasers used in photodiode linearity test
amplifiers; OSC: oscilloscope (Lecroy); Dashed line box: homodyne detector.
Figure 5.9: HD output waveform under the balanced condition at an LO power of 0.786
mW. Horizontal scale: 50 ns/div. Vertical scale: 50 mV/div. The square box on this
graph indicates one cycle.
positive and negative signals cancel out. To quantify how good the subtraction is,
the common mode rejection ratio (CMRR) can be estimated.
Chapter 5. Performance of the Homodyne Detector 65
CMRR is used to characterize the subtraction ability of the HD while it rejects
DC and preserves AC of the two input signals. Ideally, one expects the HD output
Vo = A�V1 − V2�, where V1 and V2 (voltage or current) are input signals. However,
for a practical HD, the output Vo can be described as
Vo = A1�V1 − V2� + A2
2�V1 + V2� (5.1)
where A1 is the rejection mode gain and A2 is the common mode gain (typically
smaller than A1). The CMRR is defined as
CMRR = 10 log10�A1
A2
�2 = 20 log10 �A1
A2
�. (5.2)
If the input and output signals are represented in power (i.e. V1, V2, and Vo are
power inputs and output), CMRR is defined as 10 log10 �A1
A2�.
To estimate CMRR experimentally, several approximations are made.
• If only one photodiode is illuminated and the other is blocked (i.e. V1 � 0, V2 =0), output Vo1 is
Vo1 = A1V1 + A2
2V1 � A1V1 (5.3)
where A1 � A2 is assumed considering that the rejection mode gain is far
larger than the common mode gain for a balanced receiver.
• When both photodiodes are both illuminated (i.e. V1 = V2), output Vo2 is
Vo2 = A1�V1 − V2� + A2
2�V1 + V2� � A2
22V1 = A2V1 (5.4)
where V1 = V2 (i.e. perfectly balanced signal inputs) is assumed.
If V1 is the same in the two cases, ratio of �A1
A2� can be obtained from �Vo1
Vo2�.
Under this particular condition in Fig. 5.9, Vo1 = 15 V 2 and Vo2 � 20 mV (by read-
ing the peak-to-peak voltage in Fig. 5.9). CMRR can be obtained by 20 log10 � 150.02 �
2It is estimated from the average optical power shining on one photodiode 0.786�2 = 0.393 mW, pulseduty cycle = 50 %, photodiode responsivity η = 0.90 A/W, and the HD circuit gain GTI =2.2� 104 V/A.Output HD voltage when only one photodiode is illuminated will be 0.393 mW/50% �η �GTI = 15 V
Chapter 5. Performance of the Homodyne Detector 66
= 58 dB. Note that, Vo1 cannot be measured directly by blocking one photodiode,
since this high voltage will saturate the HD circuit.
2. 50 μs is chosen as one frame to measure the HD output voltages (shown in Fig.
5.10), while there are 500 pulse cycles in each frame. The main reason to make
measurement within a very short time is to avoid the intensity drift introduced by
the system instability and environmental influences (see Section 4.3.5).
3. Step 2 is repeated under different LO powers.
4. Oscilloscope noise is measured in the absence of signal input.
Figure 5.10: One measurement frame at an LO power of 0.4 mW. Horizontal scale: 10
mV/div, Vertical scale: 5 μs/div.
Data processing
The following data processing is applied to the original waveform in Fig. 5.10.
Chapter 5. Performance of the Homodyne Detector 67
1. I break each frame into 500 segments of equal length, named S�i�.�i = 1,2, ...500)
Each segment S�i� corresponds to 100 ns, which is the period of the pulsed LO.
These segments, having the same time span, are folded onto each other, as shown
in Fig. 5.11 (a).
Figure 5.11: Data processing procedure (LO = 0.77 mW). (a) 500 original curves (one
frame) S; (b) Background curve (i.e., the average curve) of S; (c) 500 processed curves
(one frame) T .
Chapter 5. Performance of the Homodyne Detector 68
2. As shown in Fig. 5.11 (a), S�i� exhibits a DC offset in which the voltages are not
zero at the non-pulsed region (0-15 ns and 70-100 ns), caused by the HD circuit and
residual signals (peaks at 20 ns and 65 ns) due to different response functions of
the two photodiode (see Section 4.3.2). I calculate the average voltage of all curves
in S�i� as the background (shown in Fig. 5.11 (b) ). Processed pulses are obtained
by subtracting the background from S�i�, named T �i� (shown in Fig. 5.11 (c)).
3. For each processed curve T �i�, noise is calculated by adding all voltages within the
pulsed region (from 15 ns to 70 ns), named N�i�, by a similar approach in Ref. [5].
4. Variance of N�i� at each LO power is obtained as the HD noise variance.
5. The oscilloscope noise is measured in the same way in the absence of input to the
oscilloscope channel.
Results
HD noise variance and shot noise variance are plotted as a function of the LO power in
Fig. 5.12. Shot noise is linearly dependent on the LO power. The HD is 10-times shot-
noise limited at an LO power of 5.4�108 photons/pulse (0.7 mW) in the time domain.
Here, the oscilloscope noise (13 % of the electronic noise) is included in the electronic
noise. The results with pulsed LO should not be directly compared to those obtained
with CW LO, because we adopt a data processing technique that average noises within
a 55 ns time window in each cycle.
In GMCS QKD, Bob needs to measure the electric field quadrature of each signal
pulse individually. In the test of shot noise when vacuum is sent to the signal port, one
needs to verify that each pulse yields only one quadrature value. As a simple way to
check, the correlation coefficient (CC) between adjacent pulses is evaluated. At a specific
LO power of 0.77 mW, I perform HD noise measurement 10 times and combine those
noises to obtain a larger sample size NLarge�j��j = 1,2, ...,5000�. Two arrays X�k� and
Chapter 5. Performance of the Homodyne Detector 69
10−3
10−2
10−1
100
101
10−3
10−2
10−1
100
LO power (mW)
No
ise
vari
ance
(V
2 )
HD noiseShot noise
Electronic noise
10 dB
Figure 5.12: HD noise variance and shot noise variance as a function of the pulsed LO
power in the time domain. The red line has a slope of 1.
1. Same as Step 1 in the time domain measurement in Section 5.3.2 , the system has
to be calibrated to a well-balanced condition.
2. Noise power is measured from DC to 100 MHz first (shown in Fig. 5.17). There
are peaks at DC, 10 MHz, and higher harmonics of the repetition rate. The DC
component is mainly due to the pink noise and DC offset (see the time domain
data processing step 2 in Section 5.3.2). Those 10 MHz harmonic frequencies are
mainly contributed by residual signal power due to the incomplete subtraction of
the positive and negative signals.
Chapter 5. Performance of the Homodyne Detector 74
0 20 40 60 80 100−70
−60
−50
−40
−30
−20
−10
0
10
Frequency (MHz)
No
ise
po
wer
(d
Bm
/100
kH
z)
Figure 5.17: Noise spectrum at an LO power of 0.786 mW. Frequency range: DC to 100
MHz. Resolution bandwidth: 100 kHz.
3. CMRR measurement in the frequency domain
Direct measurement of CMRR in the frequency domain can be obtained by measur-
ing the noise power at the repetition rate (10 MHz) when (1) both two photodiodes
have incident optical powers (shown in Fig. 5.18 (a), this peak at 10 MHz is min-
imized by carefully balancing the two channels); and (2) only one photodiode has
incident optical power while the other photodiode is blocked (shown in Fig. 5.18
(b)). Note that, CMRR can not be directly measured at high LO powers. Ow-
ing to the huge trans-impedance gain (2.2�104 V/A, see Section 4.3.3), the HD is
easily saturated when only one photodiode is illuminated. In this experiment, the
maximum LO to avoid saturation is 49.4μW and I choose an LO power of 24.56μW
in the particular measurement shown in Fig. 5.18.
4. Noise spectrum measurement
In Fig. 5.17, the peaks at 10 MHz and its harmonics are not mainly contributed
by the shot noise. To measure shot noise, a frequency span from 5 MHz to 6 MHz
Chapter 5. Performance of the Homodyne Detector 75
Figure 5.18: Noise spectrum at an LO power of 24.56 μW when (a)two photodiodes are
illuminated; (b)one photodiode is blocked. Resolution bandwidth: 100 kHz
(far from the peaks) is chosen. This noise measurement is repeated at different LO
powers.
5. Spectrum analyzer noise is measured in the same way of step 4 in the absence of
input signal.
Chapter 5. Performance of the Homodyne Detector 76
Figure 5.19: Noise spectra at different LO powers. Frequency span: 5 to 6 MHz. Reso-
lution bandwidth: 10 kHz. LO powers are 0.0029, 0.0072, 0.0142, 0.0292, 0.0458, 0.0721,
0.1136, 0.1784, 0.2920, 0.4580, 0.7180, 1.1340, 1.7760, 2.9200 mW from the lowest curve
to the highest curve, respectively.
Results
From Fig. 5.18, the CMRR is obtained to be 54.33 dB by finding the ratio of powers at
10 MHz of the two cases, which is better than 45 dB in Ref. [5] measured at low LO
powers (the exact power is not given).
Noise spectra at different LO powers are shown in Fig.5.19. I integrate the spectral
noise under each curve over this 1 MHz frequency span. In Fig. 5.20, the noise power
is plotted as a function of the LO power. Shot noise is linearly dependent on the LO
power. The HD is 10-times shot-noise limited at an LO power of 1.54 mW (1.2�109
photons/pulse). The noise of the RF spectrum analyzer (6% of the electronic noise) is
included in the electronic noise.
Chapter 5. Performance of the Homodyne Detector 77
10−3
10−2
10−1
100
101
10−9
10−8
10−7
10−6
10−5
LO power (mW)
No
ise
po
wer
(m
W)
HD noiseShot noise
Electronic noise
10 dB
Figure 5.20: Noise power as a function of the LO power in the frequency domain. The
red line has a slope of 1.
With pulsed LO, HD noise measurements are performed in the time and the frequency
domains. In the time domain, to remove DC offset and residual signals, we performed
data processing (see Section 5.3.2), which applies a window of 55 ns in the time domain.
In the frequency domain, a 1-MHz frequency span is chosen to measure the spectral
noise. Different schemes employed in the two domains make it difficult to compare the
shot-noise-to-electronic-noise ratio with the pulsed LO.
5.4 Conclusions and discussions
In this chapter,the HD performance is tested by measuring HD noise as a function of
the LO power in both time and frequency domains. The main results are summarized as
follows.
1. The HD has a bandwidth of � 100 MHz. It is of the same order as the broad-
Chapter 5. Performance of the Homodyne Detector 78
est bandwidth HDs working at non-telecommunication wavelengths reported by
other groups [5, 30-32]. In the telecommunication wavelength region, no group has
reported HDs with broader bandwidths for use in quantum measurements.
2. With CW LO, shot noise is verified to be linearly dependent on the LO power in
the time/frequency domains. Shot noise can be above electronic noise by 10 dB at
2.6-2.8 mW LO powers. Shot-noise-to-electronic-noise-ratios are in good agreement
in the two domains. The measurement with CW light is just a preliminary test of
the HD and will not be used in future real GMCS QKD experiments.
3. With pulsed LO running at 10 MHz, shot noise is tested to be linearly dependent
on the LO power in the time/frequency domains. By using this HD, future high
speed GMCS QKD is able to operate at a repetition rate of 10 MHz, which is 1-2
orders of magnitude higher than current reported GMCS QKD systems [1, 43]. The
expected key generation rate (a few Mbits/s) is of the same order of magnitude as
the world-fastest single photon QKD experiments [4, 46].
In summary, for the first time, a �100 MHz broad bandwidth HD in the telecommu-
nication wavelength region is reported. At a pulse repetition rate of 10 MHz, a 10-times
shot-noise limited HD performance can be achieved at an LO of 5.4 � 108 photons per
pulse. With this high-speed HD, future GMCS QKD key rate is expected to achieve a
few Mbits/s over a short distance.
In future, HD can be improved in the following ways.
1. Photodiode pair that is fabricated under the same condition [51] can be used to
eliminate the residual signal due to different photodiode response functions. This
will be helpful to improve the subtraction of the HD and achieve a better shot-
noise-to-electronic-noise-ratio by using a higher LO power without saturating the
HD. With a well-matched photodiode pair, we expect to use an LO pulse containing
Chapter 5. Performance of the Homodyne Detector 79
1010 − 1011 photons, which might improve the current shot-noise-to-electronic-noise
ratio by 1-2 orders of magnitude. 3
2. Electronic noise of a HD will contribute to the excess noise and reduce key rate. In
future, to reduce electronic noise, we could cool the amplifiers and the photodiode.
Furthermore, we can choose amplifiers with lower gains, since the electronic noise
scales with gain (see Section 4.3.1). To ensure the shot noise can be detected, a
stronger LO power will be required, because HD output is proportional to EL (see
Section 2.2.1). To increase the LO power without saturating the HD circuit, the
problem of the residual signal due to different photodiode response functions should
be solved first.
3. Instead of the data processing in Section 5.3.2, filtering DC component by a high
pass filter and harmonic frequencies at laser repetition rate by notch filters can be
used to remove the residual signal and HD circuit DC offset (shown in Fig. 5.11 (b)),
which is suggested by Prof. Lvovsky. This will not improve the HD performance
directly but will avoid the trouble of implementing the data processing.
4. HDs based on integrated circuits (IC) have an advantage over those based on dis-
crete circuits. The main advantages of an IC are: (1) components are built in
a compact way and the parasitic impedance can be reduced; (2) a good quality
control and repeatable performance can be achieved. However, developing the HD
based on IC is also challenging: (1) designing the interface between commercial
photodiodes and IC might be difficult; (2) a custom IC may lack flexibility for
corrections and incremental improvements. Although there are challenges, it still
3This can be roughly estimated from Fig. 4.9 in Section 4.3.3 and Fig. 5.11 in Section 5.3.2 (c). Thelinear region of the HD electronic amplifier is at least 2V obtained from Fig. 4.9. If the residual signalis neglected using a well-matched photodiode pair, shot noise magnitude can be 2V without saturatingthe HD, which is 2 orders of magnitude greater than 20mV in Fig. 5.11 (c) in Section 5.3.2 at an LO of6�108 photons/pulse (0.77 mW). Therefore, we expect to use 6� 1010 photons/pulse without saturatingthe HD by employing a perfectly matched photodiode pair.
Chapter 5. Performance of the Homodyne Detector 80
might be a promising direction for further improving HD performance.
Chapter 6
Conclusion and Future Work
6.1 Significance and contribution
Pulse-resolved balanced homodyne detection has attracted a great attention for its appli-
cation in quantum information and quantum optics [73]. A broadband and pulse-resolved
HD in the telecommunication wavelength region used in GMCS QKD has been developed
and tested in this thesis. Table 6.1 compares the performance of our HD and the HD
from Hirano’s group, which has the broadest bandwidth in quantum optics and quan-
tum information applications. The bandwidth of our HD has achieved the same order
of magnitude as that in Ref. [5]. HD subtraction performance (indicated by CMRR) of
our HD is 9 dB higher (Note that, authors of Ref. [5] measured the CMRR using a low
LO power but they did not specify their LO power. The comparison might not be made
with the same LO power).
In Ref. [5], squeezed state is measured in both time and frequency domains. During
their measurement, pulses are identical when a particular phase between LO and signal is
fixed. Therefore, measurement in the time domain is not the only way to characterize the
squeezed state. Measuring the noise in the frequency domain can also used to determine
the uncertainty of squeezed states.
81
Chapter 6. Conclusion and Future Work 82
In contrast to the squeezed state measurement, in GMCS QKD experiments, signal
pulses should be measured individually since they are modulated with Gaussian dis-
tributed keys. Hence it is very important for us to realize the pulse measurement in
the time domain, which is demonstrated in the HD noise correlation measurement. Our
experiment shows the correlation coefficient of adjacent quadratures is 0.034, which is on
the same order of magnitude as Ref. [5] (0.04) and Ref. [57] (0.07).
With our 100 MHz bandwidth and pulse-resolved HD, we expect to perform GMCS
QKD experiments at a repetition rate of 10 MHz, which will improve the GMCS QKD
key rate per second by 1-2 orders and will be of the same order as the key rate achieved
by current high speed single photon QKD experiments [4, 46].
For the 20-km GMCS QKD work based on an existing system with a low speed
HD (developed by Dr. Bing Qi and Lei-Lei Huang), two conference papers have been
accepted by the Conference on Lasers and Electro-optics (CLEO/QELS 2008) and SPIE
Optics + Photonics 2008[6, 7]. High speed HD work (done by me, under the daily
supervision of Dr. Bing Qi, and in frequency discussions with Profs. Li Qian and Hoi-
Kwong Lo) has been presented in QuantumWorks 2009 (poster)[84]. A journal paper
is under preparation. Collaborated work on high speed random number generators, in
which I worked on preliminary random number tests with NIST Statistical Test Suite,
has been accepted by 9th Asian Conference on Quantum Information Science [85].
Table 6.1: HD peformance comparison between our group and Ref. [5]
Our HD Ref. [5]
Wavelength 1550 nm 1064 nm
Bandwidth �100 MHz � 250 MHz
CMRR 54 dB (LO = 24.56 μW) 45 dB (low LO power)
Chapter 6. Conclusion and Future Work 83
6.2 Future work
In this thesis, we developed a high speed shot-noise limited HD in the telecommunication
wavelength region. There are a few practical problems we can try to solve, such as
different photodiode response functions. For a fully telecommunication fiber-based high
speed GMCS QKD, an optical system and a control system should be investigated in
future.
1. Different photodiode response functions
In high speed HD construction, a very practical problem is the residual signal
due to different response functions of the photodiodes. To overcome this problem,
there are a few feasible methods. First, a well-matched photodiode pair that two
photodiodes are fabricated under idenetical condition can be used to minimize the
residual signal. Second, a HD based on one photodiode can be studied, which we
call a self-differencing scheme.
This self-differencing scheme is first introduced by Ref. [86] to construct high speed
single photon detectors. If we use this idea in HD, the schematic is shown in Fig.
6.1,
(a) The signal and local oscillator interfere at the left 50/50 optical splitter.
(b) We can introduce a time delay between the resulting two pulses to separate
them in the time domain.
(c) The two pulses are recombined in the right 50/50 optical splitter. Now we
should expect two separate optical pulses (shown as the red pulses). We call
them pulse 1 and pulse 2.
(d) We use one photodiode to detect both optical pulses, converting them into
two electrical pulses (shown as the lower right two blue pulses).
Chapter 6. Conclusion and Future Work 84
Figure 6.1: A self-differencing scheme in homodyne detection. Red pulses are optical
pulses and blue pulses are electrical pulses.
(e) The two electric pulses are then splitted into four electric pulses by the electric
splitter. We call them pulse 1’, 2’, 1”, 2”.
(f) We introduce another time delay which is identical to the optical delay in-
troduced in Step (b) by an electric delay. The purpose is to align the second
pulse in the upper path (pulse 2’) and the first pulse in the lower path (pulse
1”) in the time domain.
(g) We perform a subtraction between the two paths. We expect to receive a large
negative pulse (pulse 1’) and a large positive pulse (pulse 2”). In the middle
of these two strong pulses we may observe the desired result (pulse 1” - pulse
2’).
(h) Output signal will be amplified by electronic amplifiers (not shown).
The advantages of this scheme are
(a) All the components (except the electronic amplifiers) are passive with a high
Chapter 6. Conclusion and Future Work 85
speed and low noise.
(b) We use only one photodiode. Therefore we can eliminate most of photodiode
mismatch discussed in Section 4.3.2.
(c) Most compenents are commercial and the implementation is simple.
But there are still a few challenges in this scheme,
(a) All the passive devices should not introduce much distortion to the shapes of
electrical pulses.
(b) With a huge gain of subsequent electronic amplifier, the pulses 1’ and 2” will
saturate the electronic amplifiers. One possible solution is to let electronic
amplifiers work in a gating mode (i.e., it is operating when the incoming signal
is the subtraction of pulses 1” and 2’). An alternative method is to carefully
choose the repetition rate to overlap pulse 1’ and pulse 2” from the previous
cycle in the time domain. This will also double the effective repetition rate.
(c) The loss of this system has to be calibrated carefully.
This novel self-differencing scheme is worth trying to solve the photodiode mismatch
problem.
2. Local oscillator power
The optimal LO power has to be investigated systematically. The excess noises
from Bob’s system have two sources: HD electronic noise Nele and noise associate
with the leakage photon from LO to signal Nleak. To suppress Nele, a strong LO
should be chosen in order to improve the shot-noise-to-electronic-noise ratio. How-
ever, controlling the leakage photon from the LO beam to the signal beam is more
technically challenging with a strong LO. Therefore, a tradeoff between the two
noises has to be made when we choose a proper LO power.
Chapter 6. Conclusion and Future Work 86
3. Optical scheme
Time-multiplexing [43], time-frequency-multiplexing [66] and polarization-frequency-
multiplexing [1] schemes are existing techniques to suppress the excess noise due to
leakage interference of LO and leakage from LO to signal [1, 43, 44]. It is necessary
to conduct more research to select an optimal scheme for future high speed GMCS
QKD.
To achieve a high sped GMCS QKD system in real time operation, improving the
speed of the data acquisition is still in demand. To control the system excess noise
induced by the environment, the system stability should be investigated. In parallel
with these development, new algorithms, which aim at achieving farther communication
distance and higher secret key generation rates based on more efficient reconciliation are
meaningful research directions.
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