Cubitt, Toby Stanly and Chen, Jianxin; and Harrow, Aram W. (2011) Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel. IEEE transactions on information theory, 57 (12). pp. 8114-8126. ISSN 0018-9448
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Official URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6094278
Abstract
The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Additivity violation;Channel coding;Communication channels; Information rates;Quantum theory;Superactivation;Zero-error capacity |
| Subjects: | Sciences > Physics > Mathematical physics |
| ID Code: | 14959 |
| References: |
[1] A. S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory, vol. 44, pp. 269–273, 1998, (arXiv:quant-ph/9611023). [2] B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A, vol. 56, p. 131, 1997. [3] I. Devetak, “The private classical capacity and quantum capacity of a quantum channel,” IEEE Trans. Inf. Theory, vol. 51, no. 1, p. 44, Jan. 2005, (arXiv:quant-ph/0304127). [4] P. W. Shor, “The quantum channel capacity and coherent information,” presented at the MSRI Seminar, Nov. 2002. [5] S. Lloyd, “Capacity of the noisy quantum channel,” Phys. Rev. A, vol. 55, p. 1613, 1996. [6] D. P. DiVincenzo, P. W. Shor, and J. A. Smolin, “Quantum channel capacity of very noisy channels,” Phys. Rev. A, vol. 57, p. 830, 1998, (arXiv:quant-ph/9706061). [7] M. B. Hastings, “A counterexample to additivity of minimum output entropy,” Nature Phys., vol. 5, 2009, (arXiv:0809.3972 [quant-ph]). [8] A. J.Winter and P. Hayden, “Counterexamples to the maximal p-norm multiplicativity conjecture for all _ ,” Commun. Math. Phys., vol. 284, no. 1, p. 263, 2008, (arXiv:0807.4753 [quant-ph]). [9] T. Cubitt, A. W. Harrow, D. Leung, A. Montanaro, and A. Winter, “Counterexamples to additivity of minimum output p-rényi entropy for p close to 0,” Commun. Math. Phys., vol. 284, p. 281, 2008, (arXiv:0712.3628 [quant-ph]). [10] G. Smith and J. Yard, “Quantum communication with zero-capacity channels,” Science, vol. 321, p. 1812, 2008, (arXiv:0807.4935 [quantph]). [11] P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Superactivation of bound entanglement,” 2000, arXiv:quant-ph/0005117. [12] K. Li, A. Winter, X. Zou, and G. Guo, “Nonadditivity of the private classical capacity of a quantum channel,” 2009, arXiv:0903.4308[quant-ph]. [13] G. Smith and J. Smolin, “Extensive nonadditivity of privacy,” 2009, arXiv:0904.4050 [quant-ph]. [14] C. E. Shannon, “The zero-error capacity of a noisy channel,” IEEE Trans. Inf. Theory, vol. IT-2, no. 1, pp. 8–19, Jan. 1956. [15] J. Körner and A. Orlitsky, “Zero-error information theory,” IEEE Trans. Inf. Theory, vol. 44, no. 6, p. 2207, Nov 1998. [16] R. A. C. Medeiros and F. M. de Assis, “Quantum zero-error capacity,” Int. J. Quant. Inf., vol. 3, p. 135, 2005. [17] S. Beigi and P. W. Shor, “On the complexity of computing zero-error and holevo capacity of quantum channels,” 2007, arXiv:0709.2090[quant-ph]. [18] R. Duan and Y. Shi, “Entanglement between two uses of a noisy multipartite quantum channel enables perfect transmission of classical information,” Phys. Rev. Lett., 2008, (arXiv:0712.3700 [quant-ph]). [19] R. Duan, J. Chen, and Y. Xin, “Unambiguous and zero-error classical capacity of noisy quantum channels,” (manuscript in preparation). [20] R. Hartshorne, Algebraic Geometry. New York: Springer-Verlag, 1977. [21] I. R. Shafarevich, Basic Algebraic Geometry 1, 2nd, revised and expanded ed. New York: Springer-Verlag, 1994. [22] T. Cubitt, A. Montanaro, and A. Winter, “On the dimension of subspaces with bounded schmidt rank,” J. Math. Phys., vol. 49, p.022107, 2008,(arXiv:0706.0705[quant-ph]). [23] J. Harris, Algebraic Geometry. New York: Springer-Verlag, 1992. [24] D. DiVincenzo, T. Mor, P. W. Shor, J. Smolin, and B. Terhal, “Unextendible product bases, uncompletable product bases and bound entanglement,” Commun. Math. Phys., vol. 238, no. 3, p. 379, 2003. [25] R. Bhat, “A completely entangled subspace of maximal dimension,” Int. J. Quant. Inf., vol. 4, no. 2, p. 325, 2006. [26] J. Oppenheim, “For quantum information, two wrongs can make a right,” Sci. Perspectives, vol. 321, no. 5897, p. 1783, 2008. [27] R. Duan, “Superactivation of zero-error capacity of noisy quantumchannels,” 2009, arXiv:0906.2527 [quant-ph]. |
| Deposited On: | 24 Apr 2012 12:03 |
| Last Modified: | 24 Apr 2012 12:03 |
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