On complementary channels and the additivity problem

Abstract

We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the mutiplicativity/additivity conjecture for a class of CP maps implies its validity for complementary maps. The class of CP maps complementary to entanglement-breaking ones is described and is shown to contain diagonal CP maps as a proper subclass, resulting in new class of CP maps (channels) for which the multiplicativity/additivity holds. Covariant and Gaussian channels are discussed briefly in this context.

11 pages; references added, typos corrected

References in corpus (5)

• General Entanglement Breaking Channels
• Properties of Conjugate Channels with Applications to Additivity and Multiplicativity
• On some additivity problems in quantum information theory
• An application of a matrix inequality in quantum information theory
• Additivity for transpose depolarizing channels

Cited by in corpus (27)

• An Invitation to Quantum Incompatibility
• Contractivity of positive and trace preserving maps under $L_p$ norms
• Properties of Conjugate Channels with Applications to Additivity and Multiplicativity
• Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence
• Comments on Hastings' Additivity Counterexamples
• Another Short and Elementary Proof of Strong Subadditivity of Quantum Entropy
• Nonadditivity effects in classical capacities of quantum multiple-access channels
• On Weyl-covariant channels
• Selfcomplementary quantum channels
• Game-theoretic characterization of antidegradable channels
• Some Open Problems in Quantum Information Theory
• Towards a state minimizing the output entropy of a tensor product of random quantum channels
• On approximation of quantum channels
• Beyond islands: A free probabilistic approach
• Reversibility of a quantum channel: general conditions and their applications to Bosonic linear channels
• Computational Distinguishability of Quantum Channels
• Additivity rates and PPT property for random quantum channels
• Conditions for equality between entanglement-assisted and unassisted classical capacities of a quantum channel
• Complementarity and additivity for depolarizing channels
• Strong* convergence of quantum channels
• Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel and its applications
• On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements
• A relation between completely bounded norms and conjugate channels
• A criterion for coincidence of the entanglement-assisted classical capacity and the Holevo capacity of a quantum channel
• On quantum states with a finite-dimensional approximation property
• Private quantum codes: introduction and connection with higher rank numerical ranges
• On the structutre of the algebra generated by the non-commutative operator graph demonstrating superactivation for a zero-error capacity