Www.bris.ac.uk Introduction to Photonic Quantum Logic QUAMP Summer School SEPT 2006 J. G. Rarity University of Bristol [email protected] EU FET:

Introduction to PhotonicIntroduction to PhotonicQuantum Quantum

LogicLogic QUAMP Summer School SEPT 2006QUAMP Summer School SEPT 2006

J. G. RarityJ. G. RarityUniversity of BristolUniversity of Bristol

[email protected]@bristol.ac.uk

EU FET: QAPEU FET: QAP

Bristol: Daniel Ho, J. Fulconis, J. Duligall, C. Hu, R. Gibson, O Alibart, J. O’Brien Bath: William Wadsworth, Sheffield: M. Skolnick, D. Whittaker, M. Fox, J. TimpsonHP Labs: W. Munro, T. Spiller, K. Harrison

EPSRCEPSRC1-phot1-phot

FP6:IP FP6:IP SECOQCSECOQC

www.ramboq.orgwww.ramboq.org

Structure– What is light?– Decoherence of photons– Single photon detection– Encoding bits with single photons and single bit manipulation.– Linear logic– Entangled state sources– Single photon sources– Quantum Cryptography

The electro-magnetic spectrum

Optical Photon energy Eph=hf>>KT

λ=1.5umEph=0.8eV

λ=0.33umEph=4eV

V+

Particlelike Wave-like during propagation

Particlelike

Decoherence of photons: associated with loss

• Storage time in fibre 5μs/km, loss 0.17 dB/km (96%)

• Polarised light from stars==Storage for 6500 years!

Photon is absorbed in the avalanche region to create an electron hole pair

Electron and hole are accelerated in the high electric field

Collide with other electrons and holes to create more pairs

With high enough field the device breaks down when one photon is absorbed

Photon counting using avalanche photodiodes

Photon absorbed

Commercial actively quenched detector module using Silicon APDEfficiency ~70% (at 700nm)Timing jitter~400ps (latest <50ps)Dark counts <50/secwww.perkinelmer.com

InGaAs avalanche detectors:Gated modules operation at 1550nmLower efficiency ~20-30%Higher dark counts ~1E4/secAfterpulsing (10 us dead time)www.idquantique.com

Other detectors

• The Geiger mode avalanche diodes count one photon then switch off for a dead time before they are ready to detect another-NOT PHOTON NUMBER RESOLVING

• Photon number resolving detectors may become available in the near future:– Cryogenic superconducting to resistive transitions Jaspan et al

APL 89, 031112, 2006– Impurity transitions in heavily doped silicon (Takeuchi)

Interference effectswith single photons

Phaseplate

Beamsplitter50:50

Mirror

D(1)

D(0)

Mirror

D(0)CountRate

0 Thicknessof phase plate

Single photon can only be detected in one detectorHowever interference pattern built up from many individual countsP. Grangier et al, Europhysics Letters 1986

L

U

In the interferometer we have superposition state

)11(2

1L

iU

e

2/)sin1()1(

2/)sin1()0(

y probabilitDetection

1 10

generalIn

1)(0)1(21

21,

2

)11(2

1

2

22

P

P

eiie

tir

e

iiout

Li

U

After the interferometer:

Phaseplate

Beamsplitter50:50

Mirror

D(1)

D(0)

Mirror

D(0)CountRate

0 Thicknessof phase plate

Encoding one bit per photon and single qubit rotations

Encoding single photons using two polarisation modes Superposition states of ‘1’ and ‘0’

|Ψ>= α|0> +β|1> Probability amplitudes α , β

Detection Probability: |α|2

Single photon encoding showing QBER<5.10-4

(99.95% visibility)

-20 0 20 40 60 80 100 120 140 160 180 200

102

103

104

105

Gat

ed c

ount

rat

e

/2 plate angle

2QUBIT logic: Photonic CNOT Gate.

ccccttin

1010

ctcctcctcctcout10011100

D(1)

PBS D(0)

Targeta bt t| H>+ | >V

Controla bc c| H>+ | >V

QR is a quantum polarisation rotatorRotates polarisation if control is vertically polarisedDoes nothing if control is Horizontally polarised

Requires non-linearity at single photon level: Atoms: Turchette and Kimble PRL1995, Solid state: J. P. Reithmaier/ A. Forchel, NATURE 432, Nov 2004.

Bennett and Brassard 1984Secure key exchange using quantum cryptography

Sendsno. bit pol.1 1 452 0 453 0 04 1 455 1 06 0 457 1 45…1004 0 451005 1 0….3245 1 45…

Receivesno. Bit Pol.246 1 451004 0 452134 0 03245 0 04765 1 05698 0 45

Multi-qubit gates

Hong Ou Mandel interference effect

ctctout

tccctt

ctin

irtirtrt

irtirt

1,11,111)(

111 : 111

11

Dip Mandel-Ou-Hong

22

Hong, Ou, MandelPRL 1987

KLM gate

ct

ctctout

ctin

irtirtrt

1131

1,11,111)(

11

22

Demonstration of an all-optical quantum controlled-NOT gate

Knill et al Nature 409, 46–52 (2001)J L O’Brien et al, Nature 426, 264 (2003) / quant-ph/0403062

Polarisation KLM gate

Parity Measurement

Parity and conditional CNOTKnill et al Nature 409, 46–52 (2001)

Pittman et al (2002) PRL 88, 257902

Not 100% efficient but Up to 50%

NotesTarget V-->H+V Control V-->H+VParity-->HH+VV -45--> H(H+V)-V(H-V) Confirm click is H-->(H-V) out -45--> |H>Confirm click is V-->(H+V) out -45--> |V>

Target V-->H+V Control H-->H-VParity-->HH-VV -45--> H(H+V)+V(H-V) Confirm click is H-->(H+V) out -45--> |V>

A ‘scalable’ 2-qubit CNOT gate

In the proposal Actual realisationTruth tableFidelity ~0.8

S. Gasparoni, J-W Pan, P. Walther, T. Rudolph, and A. Zeilinger, Phys. Rev. Lett. 93, 020504 (2004)

IST-2001-38864: RAMBOQ

Optical Cluster State ComputingP. Walther et al Nature 434, 169-176 (2005)