The minimum entropy output of a quantum channel is locally additive

Abstract

We show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the additivity conjecture, makes this result quite surprising. In particular, it indicates that the non-additivity of the minimum entropy output is a global effect of quantum channels.

Shorter Version, further simplifications of proofs

References in corpus (11)

• The second laws of quantum thermodynamics
• The Quantum Chernoff Bound
• Quantum Communication With Zero-Capacity Channels
• Catalytic Conversion Probabilities for Bipartite Pure States
• Necessary and Sufficient Conditions for the Trumping Relation
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Comments on Hastings' Additivity Counterexamples
• Additivity of minimal entropy output for a class of covariant channels
• Entangled inputs cannot make imperfect quantum channels perfect
• The minimum entropy output of a quantum channel is locally additive
• The bosonic minimum output entropy conjecture and Lagrangian minimization

Cited by in corpus (7)

• The minimum entropy output of a quantum channel is locally additive
• Entanglement monotones and transformations of symmetric bipartite states
• Black hole microstates vs. the additivity conjectures
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula
• The minimum Renyi entropy output of a quantum channel is locally additive
• On directional derivatives of trace functionals of the form $A\mapsto\Tr(Pf(A))$
• Stability theorem of depolarizing channels for the minimal output quantum Rényi entropies