Simplifying additivity problems using direct sum constructions

Abstract

We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy and its convex closure. We show for each of them that additivity for arbitrary pairs of channels holds iff it holds for arbitrary equal pairs, which in turn can be taken to be unital. In a similar sense, weak additivity is shown to imply strong additivity for any convex entanglement monotone. The implications are obtained by considering direct sums of channels (or states) for which we show how to obtain several information theoretic quantities from their values on the summands. This provides a simple and general tool for lifting additivity results.

5 pages

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• Quantum entanglement
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• Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
• The structure of degradable quantum channels
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Comments on Hastings' Additivity Counterexamples
• Gaussian optimizers and the additivity problem in quantum information theory
• Superadditivity of private information for any number of uses of the channel
• Positivity and nonadditivity of quantum capacities using generalized erasure channels
• Entanglement of random subspaces via the Hastings bound
• Additivity and Distinguishability of Random Unitary Channels
• Capacity Estimates via comparison with TRO channels
• Towards a state minimizing the output entropy of a tensor product of random quantum channels
• Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
• Revisiting additivity violation of quantum channels
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• Partially Coherent Direct Sum Channels
• Capacities of the covariant Pauli channel
• Capacity Bounds via Operator Space Methods
• Counting atypical black hole microstates from entanglement wedges
• On the minimum output entropy of random orthogonal quantum channels
• Information-theoretic aspects of the generalized amplitude damping channel
• Additivity of quantum capacities in simple non-degradable quantum channels
• Structural Characterization And Condition For Measurement Statistics Preservation Of A Unital Quantum Operation
• Information storage and transmission under Markovian noise
• Simultaneous superadditivity of the direct and complementary channel capacities