On the number of uses of the channel needed to find positive coherent information

Toby Cubitt^a, David Elkouss^b, Will Matthews^c, Maris Ozols^a, David Pérez-García^b, Sergii Strelchuk^a

^aDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, U.K.

^bDepartamento de Análisis Matemático and Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain

^cStatistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, U.K.

The quantum capacity of a channel is given by the regularization of the coherent information of an unbounded number of uses of the channel. This regularization is necessary due to the nonadditive behaviour of the coherent information [1,2,3]. However, all results until now had shown superadditivity violations only up to a small finite number of uses [1,4]. In this talk, for any number of uses, we present a channel with zero coherent information but positive quantum capacity.

[1] D. P. DiVincenzo, P. W. Shor, and J. A. Smolin, Phys. Rev. A 57, 830 (1998).

[2] G. Smith, J. M. Renes, and J. A. Smolin, Phys. Rev. Lett. 100, 170502 (2008).

[3] M. B. Hastings, Nature Physics 5, 255 (2009).

[4] G. Smith and J. A. Smolin, Phys. Rev. Lett. 98, 030501 (2007).