On channels with positive quantum zero-error capacity having vanishing n-shot capacity
Abstract
We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n we explicitly construct low-dimensional quantum channels (=4, =2 or 4) whose quantum zero-error capacity is positive but the corresponding n-shot capacity is zero. We give estimates for quantum zero-error capacity of such channels (as a function of n) and show that these channels can be chosen in any small vicinity (in the cb-norm) of a classical-quantum channel. Mathematically, this property means appearance of an ideal (noiseless) subchannel only in sufficiently large tensor power of a channel. Our approach (using special continuous deformation of a maximal commutative *-subalgebra of ) also gives low-dimensional examples of superactivation of 1-shot quantum zero-error capacity. Finally, we consider multi-dimensional construction which gives channels with greater values of quantum zero-error capacity and vanishing n-shot capacity.
Keywords
Cite
@article{arxiv.1407.8524,
title = {On channels with positive quantum zero-error capacity having vanishing n-shot capacity},
author = {M. E. Shirokov},
journal= {arXiv preprint arXiv:1407.8524},
year = {2015}
}
Comments
20 pages, in v.2 the examples of channels are made explicit (without uncertain parameter) and their quantum zero-error capacity is estimated, in v.3 the multi-dimensional generalization is added and open questions are formulated, in v.5 some of these questions are solved