Equivalence of Additivity Questions in Quantum Information Theory

Abstract

We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. We show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entanglement of formation, are either all true or all false.

now 20 pages, replaced to add a reference, remove a reference to a claimed result about locally minimal output entropy states (my proof of this was incorrect), correct minor typos, and add more explanation for the background of these conjectures

Cited by in corpus (12)

• Quantum Channels with Memory
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• The platypus of the quantum channel zoo
• Distillable entanglement under dually non-entangling operations
• Entanglement entropy and vacuum states in Schwarzschild geometry
• Computable lower bounds on the entanglement cost of quantum channels
• Entanglement cost for infinite-dimensional physical systems
• Asymptotic quantification of entanglement with a single copy
• On the minimum output entropy of random orthogonal quantum channels
• Computable entanglement cost under positive partial transpose operations
• An upper bound on quantum capacity of unital channels
• SU(2)-equivariant quantum channels: semiclassical analysis