Demonstration of an efficient quantum Demonstration of an efficient quantum phasephase--covariant cloning and itcovariant cloning and it’’s possible s possible application to simulate an eavesdropping application to simulate an eavesdropping attack in quantum cryptographyattack in quantum cryptography

DuDu JiangfengJiangfengNov. 22, 2003Nov. 22, 2003

Cooperators :Cooperators :ZouZou Ping (Univ. of Ping (Univ. of SciSci. & Tech. of China). & Tech. of China)T. T. DurtDurt (TONA Free University of Brussels)(TONA Free University of Brussels)L. C. L. C. KwekKwek ,C. H. Oh, ,C. H. Oh, C.H.LaiC.H.Lai (National Univ. of Singapore)(National Univ. of Singapore)ArturArtur EkertEkert (DAMTP, Univ. of Cambridge)(DAMTP, Univ. of Cambridge)

OutlineOutline

IntroductionIntroductionPhasePhase--convariantconvariant cloningcloningExperimentExperimentDiscussion and conclusionDiscussion and conclusion

BackgroundBackground

Quantum Information

Computation Communication

Implement: Trapped ion, Cavity QED, NMR, JJ, Quantum dot….

Recent theoretical results (2003)Recent theoretical results (2003)

1.1. JiangfengJiangfeng DuDu and and HuiHui Li, Quantum Games of Li, Quantum Games of Asymmetric Information,Asymmetric Information, Physics Review E 68Physics Review E 68，，016124 (2003).016124 (2003).

2.2. HuiHui Li and Li and JiangfengJiangfeng DuDu, Relativistic, Relativistic--invariant invariant quantum entanglement between the spins of moving quantum entanglement between the spins of moving bodies, Physics Review A 68, 022108 (2003).bodies, Physics Review A 68, 022108 (2003).

3.3. K. Singh, D. M. Tong, K. K. Singh, D. M. Tong, K. BasuBasu, J. L. Chen, and J. F. , J. L. Chen, and J. F. DuDu，，Geometric phases for Geometric phases for nondegeneratenondegenerate and and degenerate mixed statesdegenerate mixed states，，Physics Review A 67, Physics Review A 67, (2003) 032106.(2003) 032106.

4.4. JiangfengJiangfeng DuDu, , HuiHui Li, Li, XiaodongXiaodong XuXu, , XianyiXianyi Zhou and Zhou and RongdianRongdian Han, PhaseHan, Phase--TransitionTransition--like behavior of like behavior of Quantum Games, Journal ofQuantum Games, Journal of Physics A: Physics A: Mathematical and General 36 (2003) 6551Mathematical and General 36 (2003) 6551--6562. 6562.

NMRNMR--QIP ExperimentsQIP Experiments

Quantum Logic Gates and AlgorithmQuantum Logic Gates and Algorithm–– JiangfengJiangfeng DuDu et al., et al., Physical Review APhysical Review A 63, 042302 (2001).63, 042302 (2001).–– JiangfengJiangfeng DuDu et al., et al., Physical Review APhysical Review A 64, 042306 (2001).64, 042306 (2001).–– JiangfengJiangfeng DuDu et al., et al., Physical Review A 67, 042316Physical Review A 67, 042316 (2003).(2003).

Quantum GamesQuantum Games–– JiangfengJiangfeng DuDu et al., et al., Physical Review Letters 88, 137902Physical Review Letters 88, 137902

(2002).(2002).

Geometric Phase of Mixed StatesGeometric Phase of Mixed States–– JiangfengJiangfeng DuDu et al., et al., Physical Review Letters 91, 100403Physical Review Letters 91, 100403

(2003).(2003).

StateState--dependent cloning, (submitted, 2003) dependent cloning, (submitted, 2003)

NoNo--cloning theoremcloning theorem

For unknown quantum stateFor unknown quantum stateW.K. W.K. WootersWooters and W.H. and W.H. ZurekZurek, Nature 299, 802(1982), Nature 299, 802(1982)–– An An arbitrary quantum statearbitrary quantum state can not be cloned can not be cloned

exactly.exactly.–– Security of quantum cryptographySecurity of quantum cryptography

V. V. BuzekBuzek and M. and M. HilleryHillery, , Phys.Rev.APhys.Rev.A 54, 1844 (1996)54, 1844 (1996)L.M.DuanL.M.Duan and and G.C.GuoG.C.Guo, Phys.Rev.Lett.80, 4999(1997), Phys.Rev.Lett.80, 4999(1997)

–– However, it can be cloned approximately or However, it can be cloned approximately or probabilisticallyprobabilistically

StateState--independent & Stateindependent & State--dependent clonedependent clone

Universal Quantum Cloning Universal Quantum Cloning Machine (UQCM)Machine (UQCM)

StateState--independent cloningindependent cloningV. V. BuzekBuzek and M. and M. HilleryHillery, , Phys.Rev.APhys.Rev.A 54, 1844 (1996)54, 1844 (1996)

–– StateState--independentindependent–– 33--qubit for cloning 1 to 2 qubit for cloning 1 to 2 –– Optimal Fidelity: 83.33%Optimal Fidelity: 83.33%

–– Application: the optimal device for an Application: the optimal device for an eavesdropper to attack the 6eavesdropper to attack the 6--state protocol of state protocol of quantum cryptography. QBER=1quantum cryptography. QBER=1--F=16.67%F=16.67%

UQCM ExperimentsUQCM ExperimentsExperimental Fidelities: (Experimental Fidelities: (theory: 83.33%)theory: 83.33%)–– Single photon: 81%Single photon: 81%–– Optical Fiber Amplifier: 82%Optical Fiber Amplifier: 82%–– NMR: 58%NMR: 58%

Y.F. Huang et al., Y.F. Huang et al., Phys.RevPhys.Rev. A 64, 012315 (2001). A 64, 012315 (2001)A. LamasA. Lamas--LinaresLinares et al., Science 296, 712 (2002)et al., Science 296, 712 (2002)S.FaselS.Fasel et al., et al., Phys.Rev.LettPhys.Rev.Lett. 89, 107901 (2002) . 89, 107901 (2002) H.K. Cummins et al., H.K. Cummins et al., Phys.Rev.LettPhys.Rev.Lett. 80, 4999(2002) . 80, 4999(2002)

QuntumQuntum PhasePhase--ConvariantConvariantCloning Machine (QPCCM)Cloning Machine (QPCCM)

StateState--dependent clonedependent cloneUsed to copy the states which has in priori information, it is Used to copy the states which has in priori information, it is the optimal device for an eavesdropper to attack the 4the optimal device for an eavesdropper to attack the 4--state state protocol of quantum cryptography, While UQCM can be protocol of quantum cryptography, While UQCM can be chosen to attack the 6chosen to attack the 6--state protocol. QBER=1state protocol. QBER=1--F=14.6%F=14.6%

TheoryTheoryD.BrubD.Brub et al., Phys. Rev. A 56, 3446 (1997)et al., Phys. Rev. A 56, 3446 (1997)–– 33--qubitqubit–– StateState--dependentdependent–– Slightly high fidelity: 85.4%Slightly high fidelity: 85.4%

There is no experiment existedThere is no experiment existed

In this talkIn this talk

–– Design a costDesign a cost--efficient 2efficient 2--qubit phasequbit phase--invariant cloning machineinvariant cloning machineC.NiuC.Niu and and R.B.GriffithsR.B.Griffiths, Phys. Rev. A 62, 012302 (2000), Phys. Rev. A 62, 012302 (2000)

D. Thomas and D. Thomas and J.F.DuJ.F.Du, quant, quant--ph/030972ph/030972

–– NMR realizationNMR realizationExperimental Fidelity: 84.8% and 84.8% Experimental Fidelity: 84.8% and 84.8%

(85.4%),(85.4%), it is higher than 83.33% of UQCMit is higher than 83.33% of UQCM..

–– It should be an optimal eavesdropping It should be an optimal eavesdropping attacker of BB84 QKD. attacker of BB84 QKD.

PhasePhase--covariant cloning Networkcovariant cloning Network

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Fidelity is independend of phase.

NMR quantum computingNMR quantum computing

QubitsQubitsPartially Partially deuterateddeuterated cytosine cytosine

molecule contains two protons, in a molecule contains two protons, in a magnetic field, each spin state of magnetic field, each spin state of proton could be used as a proton could be used as a qubitqubit. . Distinguish each Distinguish each qubitqubitDifferent Different LarmorLarmor frequencies (the frequencies (the

chemical shift) enable us to address chemical shift) enable us to address each each qubitqubit individually.individually.Quantum logic gates Quantum logic gates Radio Frequency (RF) fields and Radio Frequency (RF) fields and

spinspin----spin couplings between the spin couplings between the nuclei are used to implement nuclei are used to implement quantum logic gates. quantum logic gates.

ExperimentExperiment

22--QubitQubitInitial state:Initial state:

Unitary evolutionUnitary evolutionReadoutReadout

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RF Pulse sequenceRF Pulse sequence

ExperimentExperiment

We have prepared a total of 24 input equator We have prepared a total of 24 input equator states; states;

For each input state, the cloning For each input state, the cloning transformation was performed;transformation was performed;finally we measure each copy and calculate finally we measure each copy and calculate the fidelity, which is phasethe fidelity, which is phase--covariant. covariant. Experimentally, we get the mean fidelity of Experimentally, we get the mean fidelity of this phasethis phase--covariant cloning iscovariant cloning isF1=0.844 and F2=0.848, which is close F1=0.844 and F2=0.848, which is close to the optimal theoretical value 0.854.to the optimal theoretical value 0.854.

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Discussion and conclusionDiscussion and conclusion

Compared to NMR experiment for QUCMCompared to NMR experiment for QUCMH.K. Cummins et al., H.K. Cummins et al., Phys.Rev.LettPhys.Rev.Lett. 80, 4999(2002). 80, 4999(2002)

–– 33--qubit circuit is much more complicated than 2qubit circuit is much more complicated than 2--qubit circuit in a real experimentqubit circuit in a real experiment..

–– their lower fidelity 58% (not the expected 83%) their lower fidelity 58% (not the expected 83%) is is arisedarised from from decoherencedecoherence and B1 and B1 inhomogeneityinhomogeneity effects. The time to perform their effects. The time to perform their pulse sequences is at least 0.4s, close to pulse sequences is at least 0.4s, close to T2=0.72s; In our experiment, T2 is near 0.4s. T2=0.72s; In our experiment, T2 is near 0.4s. The total time to perform the The total time to perform the exprimentexpriment is about is about 5.7ms.5.7ms.

Simulate an eavesdropping Simulate an eavesdropping attackerattacker

(1)Prepare one of four BB84 states (1)Prepare one of four BB84 states (2) Then perform the phase(2) Then perform the phase--covariant cloningcovariant cloning

(3) we perform 288 experiments distinguished by 4 (3) we perform 288 experiments distinguished by 4 BB84 states and 24 rotation angles BB84 states and 24 rotation angles θθ and 3 and 3 measurement. measurement.

Symmetry of QPCCMSymmetry of QPCCM

X base y base

Mutual information (X & Y bases)Mutual information (X & Y bases)

Mutual information & QBERMutual information & QBER

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Discussion and conclusionDiscussion and conclusion

Compared to optical experiment,Compared to optical experiment,–– our result is more easier for Eve to store the our result is more easier for Eve to store the

photons and wait Alice and Bob to reveal the photons and wait Alice and Bob to reveal the bases.bases.

–– Our work clone the effectiveOur work clone the effective--pure states rather pure states rather than pure state. However, the basic idea is than pure state. However, the basic idea is general, it can be extended to other physical general, it can be extended to other physical system such as trapped ionssystem such as trapped ions……

it is the optimal device for an eavesdropper it is the optimal device for an eavesdropper to attack BB84 protocol of quantum to attack BB84 protocol of quantum cryptography.cryptography.

acknowledgmentacknowledgment

I acknowledge the support for my visiting here.I acknowledge the support for my visiting here.

The project was supported by the National The project was supported by the National Nature Science Foundation of China (Grants. Nature Science Foundation of China (Grants. No. 10075041) and funded by the National No. 10075041) and funded by the National Fundamental Research Program Fundamental Research Program (2001CB309300).(2001CB309300).