**ICE1 2014 **Workshop “Información Cuántca en España-1” -
Zaragoza, 2014

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

^{a}*Department
of Applied Mathematics and Theoretical Physics, University of
Cambridge, Cambridge CB3 0WA, U.K.*

^{b}*Departamento
de Análisis Matemático and Instituto de Matemática
Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid,
Spain*

^{c}*Statistical
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).