On superactivation of zero-error capacities and reversibility of a quantum channel

Abstract

We propose examples of low dimensional quantum channels demonstrating different forms of superactivation of one-shot zero-error capacities, in particular, the extreme superactivation (this complements the recent result of T.S.Cubitt and G.Smith). We also describe classes of quantum channels whose zero-error classical and quantum capacities cannot be superactivated. We consider implications of the superactivation of one-shot zero-error capacities to analysis of reversibility of a tensor-product channel with respect to families of pure states. Our approach based on the notions of complementary channel and of transitive subspace of operators makes it possible to study the superactivation effects for infinite-dimensional channels as well.

29 pages, extended version, Proposition 4 is strengthened, the results concerning asymptotic zero-error capacities are added (Corollaries 5-8), Lemma 7 is corrected; any comments are welcome

References in corpus (5)

• Quantum Communication With Zero-Capacity Channels
• The structure of degradable quantum channels
• Multi-mode bosonic Gaussian channels
• Reversibility conditions for quantum operations
• Reversibility of a quantum channel: general conditions and their applications to Bosonic linear channels

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