TY - JOUR

T1 - Counterexamples to additivity of minimum output p-rényi entropy for p close to 0

AU - Cubitt, Toby

AU - Harrow, Aram W.

AU - Leung, Debbie

AU - Montanaro, Ashley

AU - Winter, Andreas

PY - 2008/11

Y1 - 2008/11

N2 - Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi 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-Rényi entropy is non-additive for all p ≃ 0.11. We conjecture however that violations of additivity exist for all p < 1.

AB - Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi 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-Rényi entropy is non-additive for all p ≃ 0.11. We conjecture however that violations of additivity exist for all p < 1.

UR - http://www.scopus.com/inward/record.url?scp=53349164131&partnerID=8YFLogxK

U2 - 10.1007/s00220-008-0625-z

DO - 10.1007/s00220-008-0625-z

M3 - Article

AN - SCOPUS:53349164131

SN - 0010-3616

VL - 284

SP - 281

EP - 290

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -