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

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

2007-12-21

arxiv.org/abs/0712.3628v3

Communications in Mathematical Physics, volume 284, p281-290 (2008)

Physics

Quantum Physics

7 pages, revtex4; v2 added correct ref. [15]; v3 has more information on the numerical violation as well as 1 figure (2 graphs

Scientific paper

10.1007/s00220-008-0625-z

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.

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