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

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• On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator
• Maximum privacy without coherence, zero-error
• On errors generated by unitary dynamics of bipartite quantum systems
• Quantum non-signalling assisted zero-error classical capacity of qubit channels
• Noise is resource-contextual in quantum communication
• Information storage and transmission under Markovian noise
• Zero-error communication under discrete-time Markovian dynamics
• Simultaneous superadditivity of the direct and complementary channel capacities
• Activation of zero-error classical capacity in low-dimensional quantum systems