Entanglement-Assisted Capacity of Quantum Multiple-Access Channels

We find a regularized formula for the entanglement-assisted (EA) capacity region for quantum multiple-access channels (QMAC). We illustrate the capacity region calculation with the example of the collective phase-flip channel which admits a single-letter characterization. On the way, we provide a first-principles proof of the EA coding theorem based on a packing argument. We observe that the Holevo-Schumacher-Westmoreland theorem may be obtained from a modification of our EA protocol. We remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver, in analogy to the two-party case. In this way, we relate several previous results regarding QMACs.

[1]  John T. Lewis,et al.  An operational approach to quantum probability , 1970 .

[2]  S. Lloyd.  Capacity of the noisy quantum channel , 1996, quant-ph/9604015.

[3]  Aram W. Harrow,et al.  A family of quantum protocols , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[4]  M. Ozawa.  Quantum measuring processes of continuous observables , 1984 .

[5]  Igor Devetak.  The private classical capacity and quantum capacity of a quantum channel , 2005, IEEE Transactions on Information Theory.

[6]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[7]  Masahito Hayashi,et al.  General formulas for capacity of classical-quantum channels , 2003, IEEE Transactions on Information Theory.

[8]  Rudolf Ahlswede,et al.  Multi-way communication channels , 1973 .

[9]  P. Shor,et al.  The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information , 2003, quant-ph/0311131.

[10]  Toby Berger,et al.  Review of Information Theory: Coding Theorems for Discrete Memoryless Systems (Csiszár, I., and Körner, J.; 1981) , 1984, IEEE Trans. Inf. Theory.

[11]  Igor Devetak,et al.  Capacity theorems for quantum multiple-access channels: classical-quantum and quantum-quantum capacity regions , 2008, IEEE Transactions on Information Theory.

[12]  A. Holevo.  On entanglement-assisted classical capacity , 2001, quant-ph/0106075.

[13]  Andreas Winter,et al.  Partial quantum information , 2005, Nature.

[14]  Jon Yard.  Simultaneous classical-quantum capacities of quantum multiple access channels , 2005 .

[15]  W. Stinespring.  Positive functions on *-algebras , 1955 .

[16]  Andreas J. Winter.  The capacity of the quantum multiple-access channel , 2001, IEEE Trans. Inf. Theory.

[17]  Peter W. Shor,et al.  Fault-tolerant quantum computation , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[18]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[19]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[20]  Hoi-Kwong Lo,et al.  A tight lower bound on the classical communication cost of entanglement dilution , 2004, IEEE Transactions on Information Theory.

[21]  Peter W. Shor,et al.  Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem , 2001, IEEE Trans. Inf. Theory.

[22]  Michael D. Westmoreland,et al.  Sending classical information via noisy quantum channels , 1997 .

[23]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[24]  Alexander S. Holevo,et al.  The Capacity of the Quantum Channel with General Signal States , 1996, IEEE Trans. Inf. Theory.

[25]  Andreas J. Winter,et al.  Coding theorem and strong converse for quantum channels , 1999, IEEE Trans. Inf. Theory.

[26]  Jacob Wolfowitz,et al.  Multiple Access Channels , 1978 .