Cubitt, Toby S. and Leung, Debbie and Matthews, William and Winter, Andreas (2011) Zero-Error Channel Capacity and Simulation Assisted by Non-Local Correlations. IEEE transactions on information theory , 57 (8). pp. 5509-5523. ISSN 0018-9448
Restricted to Repository staff only until 2020.
The theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly in the presence of various classes of nonsignalling correlations between sender and receiver i.e., shared randomness, shared entanglement and arbitrary nonsignalling correlations. When the channel being simulated is noiseless, this is zero-error coding assisted by correlations. When the resource channel is noiseless, it is the reverse problem of simulating a noisy channel exactly by a noiseless one, assisted by correlations. In both cases, separations between the power of the different classes of assisting correlations are exhibited for finite block lengths. The most striking result here is that entanglement can assist in zero-error communication. In the large block length limit, shared randomness is shown to be just as powerful as arbitrary nonsignalling correlations for exact simulation, but not for asymptotic zero-error coding. For assistance by arbitrary nonsignalling correlations, linear programming formulas for the asymptotic capacity and simulation rates are derived, the former being equal (for channels with nonzero unassisted capacity) to the feedback-assisted zero-error capacity derived by Shannon. Finally, a kind of reversibility between nonsignalling-assisted zero-error capacity and exact simulation is observed, mirroring the usual reverse Shannon theorem.
|Uncontrolled Keywords:||Channel coding; Graph capacities; Quantum entanglement; Zero-error information theory|
|Subjects:||Sciences > Physics > Mathematical physics|
 C. E. Shannon, “The zero-error capacity of a noisy channel,” IRE Trans. Inf. Theory, vol. IT-2, no. 3, pp. 8–19, 1956.
 C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423, 623–656, 1948.
 J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, “Nonlocal correlations as an information-theoretic resource,” Phys. Rev. A, vol. 71, no. 2, p. 022101, 2005.
 C. H. Bennett, P. Shor, J. Smolin, and A. V. Thapliyal, “Entanglement- assisted capacity of a quantum channel and the reverse Shannon theorem,” IEEE Trans. Inf. Theory, vol. 48, no. 10, pp. 2637–2655, Oct. 2002.
 C. H. Bennett, I. Devetak, A. W. Harrow, P. W. Shor, and A. Winter, Quantum Reverse Shannon Theorem arXiv:0912.5537, 009.
 S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge University Press, 2004.
 R. A. C. Medeiros, R. Alleaume, G. Cohen, and F. M. de Assis, Quantum States Characterization for the Zero-Error Capacity 2006, arXiv:quant-ph/0611042.
 R. Duan, Super-Activation of Zero-Error Capacity of Noisy Quantum Channels arXiv:0906.2527, 2009.
 T. S. Cubitt, J. Chen, and A. W. Harrow, Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel arXiv:0906. 2547, 2009.
 T. S. Cubitt and G. B. Smith, Super-Duper-Activation of Quantum Zero-Error Capacities arXiv:0912.2737, 2009.
 W. Haemers, “On some problems of Lovász concerning the Shannon capacity of a graph,” IEEE Trans. Inf. Theory, vol. IT-25, no. 2, pp. 231–232, 1979.
 D. Leung, L. Mancinska, W. Matthews, M. Ozols, and A. Roy, Entanglement Can Increase Asymptotic Rates of Zero-Error Classical Communication Over Classical Channels arXiv:1009.1195.
 J. E. Cohen and U. G. Rothblum, “Nonnegative ranks, decompositions, and factorizations of nonnegative matrices,” Linear Alg. and Its Applic., vol. 190, p. 1, 1993.
 S. Kochen and E. P. Specker, “The problem of hidden variables in quantum mechanics,” J. Mathemat. and Mechan., vol. 17, pp. 59–87, 1967.
 A. Cabello, J. M. Estebaranz, and G. G. Alcaine, “Bell-Kochen- Specker theorem: An proof with 18 vectors,” Phys. Lett. A, vol. 212, p. 183, 1986.
 A. Peres, “Two simple proofs of theKochen-Specker theorem,” J. Phys. A: Mathemat. and Gen., vol. 24, no. 4, pp. L175–L178, 1991.
 T. S. Cubitt, D. Leung, W. Matthews, and A.Winter, “Improving zeroerror classical communication with entanglement,” Phys. Rev. Lett., vol. 104, p. 230503, 2010, arXiv:0911.5300.
 S. Beigi, “Entanglement-assisted zero-error capacity is upper bounded by the Lovász theta function,” arXiv:1002.2488, 2010.
 R. Duan, S. Severini, and A. Winter, Zero-Error Communication via Quantum Channels, Non-Commutative Graphs and a Quantum Lovász
|Deposited On:||24 Apr 2012 10:04|
|Last Modified:||06 Feb 2014 10:13|
Repository Staff Only: item control page