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arXiv · 1312.3586

On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements

M. E. Shirokov·Tatiana Shulman
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Abstract

We begin with a detailed description of a low dimensional quantum channel ($d_A=4, d_E=3$) demonstrating the symmetric form of superactivation of one-shot zero-error quantum capacity. This means appearance of a noiseless (perfectly reversible) subchannel in the tensor square of a channel having no noiseless subchannels. Then we describe a quantum channel $\Phi$ such that $\,\bar{Q}_0(\Phi)=0$ and $\,\bar{Q}_0(\Phi\otimes\Phi)\geq\log n\,$ for any $\,n\leq+\infty$. We also show that the superactivation of one-shot zero-error quantum capacity of a channel can be reformulated in terms of quantum measurements theory as appearance of an indistinguishable subspace for tensor product of two observables having no indistinguishable subspaces.

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M. E. Shirokov, Tatiana Shulman. 2013-12-12. On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements. https://arxiv.org/abs/1312.3586

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