Generating and harnessing photonic entanglement Funding: D EPAR TM ENT OF P HY SICS, U N IVERSITY O F Q UEENSLAND Rohan Dalton Michael Harvey Nathan Langford Till Weinhold Jeremy O’Brien Geoff Pryde Andrew White Stephen Bartlett Aggie Branczyk Michael Bremner Jen Dodd Andrew Doherty Alexei Geoff Pryde Quantum Technology Lab Theory Colleagues www.quantinfo.org
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Generating and harnessing photonic entanglement Funding: Rohan Dalton Michael Harvey Nathan Langford Till Weinhold Jeremy O’Brien Geoff Pryde Andrew White.
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Generating and harnessing photonic entanglement
Funding:
DEPARTMENT OF PHYSICS,UNIVERSITY OF QUEENSLAND
Rohan DaltonMichael HarveyNathan LangfordTill WeinholdJeremy O’BrienGeoff PrydeAndrew White
Stephen BartlettAggie BranczykMichael BremnerJen DoddAndrew DohertyAlexei GilchristGerard MilburnMichael NielsenTim Ralph
Geoff Pryde
Quantum Technology Lab
Theory Colleagues
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Andrew White
www.quantinfo.org
Stephen BartlettAlexei
Gilchrist
JeremyO’Brien Geoff Pryde
Rohan DaltonAgatha
Brancyzk
Nathan LangfordMichaelHarvey
Gerard Milburn Tim Ralph
TillWeinhold
Generating and harnessing photonic entanglement
Talk outline
1. Qubits • CNOT gate • Quantum process tomography • Generalized quantum measurements with photons
2. Qutrits and Qudits• Gaussian spatial modes• Constructing and measuring
qutrits• Use in quantum bit
commitment
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
www.quantinfo.org
H
V
VHH+iVH -VH+VH -iV VHRDLD-
Poincaré Sphere
Single qubits Single qubit gates
|H ( |H |V / √2
Hadamard gate
|H |H |V
Arbitrary rotation gate
? Two-qubit gates
•
Polarization qubits
C0
C1
T0
T1
C0
C1
T0
T1
CSIGN gate
phaseshift
Basic photonic CNOT
CNOT = HT + CSIGN + HT
HT HT
C0C1T0T1
Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002)
-1/3
1/3
1/3
CSIGN gate
2-photon CNOT operation
C0C1T0T1
Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002)
-1/3
1/3
1/3
CSIGN gate
bothreflected
bothtransmitted
2-photon CNOT operation
C0C1T0T1
Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002)
-1/3
1/3
1/3
CSIGN gate
2-photon CNOT operation
C0C1T0T1HWPHWP
Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002)
-1/3
1/3
1/3
CNOT gate
Control in Control out
Target in Target out
Polarization 2-photon CNOT
T. C. Ralph, quant-ph/0306190
J. L. Dodd et al., quant-ph/0306081
Concatenating CNOTs
2-photon CNOT in the context of scalable QC
•••
•••QUBITSQUBITSaa
Knill, Laflamme and Milburn, Nature 409, 46 (2001)
LINEAROPTICAL
NETWORK
•••
•••
SINGLEPHOTONSSINGLE PHOTON
DETECTION&
FEEDFORWARD
LOQC = “Linear Optics Quantum Computing”
J. L. O’Brien, G. J. Pryde, et al., Nature 426, 264 (2003)
What is the spatial mode quantum state of the photon pairs?
Conceptual Experimental Diagram
Post-select coincident photon pairs using counting electronics.Two-photon QST: all possible pairs of single-photon measurements.Analyse the spatial mode using holograms and single-mode fibres.
Spatial mode quantum state tomography
Uses holograms and single-mode fibres (SMFs):
Analyser extinction efficiency:
Spatial Mode Detector Efficiency
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
5.0 10.0 15.0 20.0
horizontal position of hologram (mm)
fibre coupling efficiency
centred
displaced
theory~1:103
Spatial mode analyzer (SMA)
Spatial mode quantum state tomography
populations
Spatial mode quantum state tomography
coherences
Spatial mode quantum state tomography
coherences
Spatial mode quantum state tomography
Re() Im()
Langford et al., quant-ph/0312072
• EOF < 0.704 • SL = 0.18 • Fψ = 0.88
Non-degenerate Qutrit |0=L |1=G |2=R
Two-qutrit quantum state tomography
• Alice should commit to a message and not be able to change it.• Bob should not be able to decode the message until Alice reveals it.• Quantum bit-commitment with arbitrarily good security is impossible• Qutrits offer the best-known BC security levels, whereas qubits do not!
• Communication between mistrustful parties
• Basis of other protocols, e.g. quantum coin flipping
0
?0
29-39-5
29-39-5
Quantum bit commitment
Step 1: Alice starts with our experimentally measured two-qutrit state.
Uses an entangled, two-part system:(a) the proof and (b) the token
subsystems.Assumption: initial state is only source of imperfection.
A Simulated Purification Protocol
Re() Im()
Spekkens and Rudolph, PRA 65, 012310 (2001) Langford et al., quant-ph/0312072
Quantum bit commitment
Step 2: Alice prepares her chosen logical bit.
Step 3: Alice sends the token to Bob (the commitment).
orthogonal two-qutrit states
non-orthogonal token states
Quantum bit commitment
Step 4: Alice sends the proof subsystem to Bob to complete the BC protocol. He decodes the message with a two-qutrit projective measurement:
Distinguishability of token states limits Alice’s control (trace-distance):
Non-orthogonal token states limit Bob’s possible knowledge gain (fidelity):
Quantum bit commitment
• Fidelity:
inaccessible to bestknown BC protocols
achievable withqubits
qutrits
p = 0.29p = 0.19p = 0.09
= p/3 + (1-p) ideal
classical
impossible
• Orthogonal two-qutrit states result in non-orthogonal reduced token states.• Ideal case provides optimal security, but simulated case still does not!
KEY POINTS
Langford et al., quant-ph/0312072
Quantum bit commitment
• Quantum process tomography of CNOT – fully characterize the process in the 2-qubit space
– high fidelity operation useful for q. info and q. physics tests
• Generalized measurement and QND – non-destructive; arbitrary strength; any basis
• Qutrit entanglement – measured, characterized for use in communications protocols