Coherent Classical Communication and Entanglement recycling in 经典通信和量子纠缠相干循环

1、Coherent Classical CommunicationAram Harrow, MITQuantum Computing Graduate Research FellowObjectiveObjective ApproachStatus Determine tradeoff curves for quantum channel coding and entanglement distillaton assisted by entanglement or classical or quantum communication.Find efficient methods to calcu

2、late and achieve these capacities.Relate different quantum protocols.Reconsider the role of classical communication in quantum information theory.Found classical and quantum capacities of unitary gates and quantum channels assisted by arbitrary amounts of entanglement.Proved super-dense coding of qu

3、antum states.Derived several new quantum protocols and related several old ones.HXZcoherentclassicalcomm.Research OverviewA. Harrow, MITA.W. Harrow and H.-K. Lo. “A tight lower bound on the classical communication cost of entanglement dilution. quant-ph/0204096, accepted IEEE-IT.C.H. Bennett, A.W. H

4、arrow, D.W. Leung and J.A. Smolin. “On the capacities of bipartite Hamiltonians and unitary gates. quant-ph/0205057, accepted IEEE-IT.A.W. Harrow and M.A. Nielsen. “Robustness of gates in the presence of noise, quant-ph/0301108, accepted PRA.A.W. Harrow. “Coherent Classical Communication. quant-ph/0

5、307091I. Devetak, A.W. Harrow and A. Winter. “A family of quantum protocols. quant-ph/0308044A.W. Harrow, P. Hayden and D.W. Leung. “Superdense coding of quantum states. quant-ph/0308221D. Bacon, A.W. Harrow and I.L. Chuang. “Efficient circuits for Clebsch-Gordon transformations. in preparationC.H.

6、Bennett, A.W. Harrow and S. Lloyd. “Universal compression via gentle tomography. in preparationInequivalent resources?One bit of quantum communication (1 qubit) can be used to send one classical bit (1 cbit) or generate one EPR pair (1 ebit).Conversely, teleportation uses two cbits and 1 ebit to sen

7、d 1 qubit.Although the above protocols are optimal, combining them uses three qubits to send one qubit.Similar inefficiencies exist throughout quantum information theory. Are they necessary?beyond qubits and cbitsLet |xix=0,1 be a basis for C2.qubit:|xiA!|xiB cbit:|xiA!|xiB|xiEcoherent cbit:|xiA!|xi

8、A|xiBebit: |Fi=2-1/2x|xiA|xiB 1 qubit 1 coherent cbit 1 cbit1 qubit 1 coherent cbit 1 ebitsources of CCCSuper-dense coding:1 qubit + 1 ebit 2 coherent cbitsDistributed unitary gates: If U is a unitary gate and U C cbits, then U C coherent cbits.Example: CNOT 1 cbit ()CNOT 1 cbit ()CNOT + ebit 1 cbit

9、 () + 1 cbit ()uses of CCCEntanglement recycling using CCC:Suppose X + C cbits Y and the classical message sent is independent of the output state. ThenX + C coherent cbits Y + C ebitsExample: teleportation with coherent communicationHXZ2 coherent cbits + 1 ebit 1 qubit + 2 ebitscoherentclassicalcom

10、m.Simple consequences2 coherent cbits = 1 qubit + 1 ebit(using entanglement catalytically)Teleportation and super-dense coding are no longer irreversible.Theres more!Super-dense coding of quantum states:1 qubit + 1 ebit 2 remote qubits (asymptotically)Single-letter expression for capacity of a unita

11、ry interaction to communicate classical or quantum data assisted by any amount of entanglement.Two minute proofs of the hashing inequality and the quantum channel capacity.Generalizations of these protocols to obtain the full trade-off curves for quantum channels assisted by a limited amount of entanglement and entanglement distillation with a limited amount of communication.ReferencesC.H. Bennett, A.W. Harrow, D.W. Leung and J.A. Smolin. “On the capacities of bipartite Hamiltonians and unitary gates. qu