Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0

Abstract

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Renyi entropies of channels are not generally additive for p>1, we demonstrate here by a careful random selection argument that also at p=0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Renyi entropy is non-additive for all p < 0.11. We conjecture however that violations of additivity exist for all p<1.

7 pages, revtex4; v2 added correct ref. [15]; v3 has more information on the numerical violation as well as 1 figure (2 graphs) - note that the explicit example was changed and the more conservative estimate of the bound up to which violations occur, additionally some other small issues are straightened out

References in corpus (2)

• Aspects of generic entanglement
• Entanglement between Two Uses of a Noisy Multipartite Quantum Channel Enables Perfect Transmission of Classical Information

Cited by in corpus (7)

• Quantum channels and their entropic characteristics
• Distillable entanglement under dually non-entangling operations
• Capacities of the covariant Pauli channel
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• Computable entanglement cost under positive partial transpose operations
• Convex Trace Functions on Quantum Channels and the Additivity Conjecture
• New constructive counterexamples to additivity of minimum output Rényi p-entropy of quantum channels