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Title: Counterexamples to additivity of minimum output p-rényi entropy for p close to 0
Authors: Cubitt, T.
Harrow, A.W.
Leung, D.
Montanaro, A.
Winter, A. 
Issue Date: Nov-2008
Citation: Cubitt, T., Harrow, A.W., Leung, D., Montanaro, A., Winter, A. (2008-11). Counterexamples to additivity of minimum output p-rényi entropy for p close to 0. Communications in Mathematical Physics 284 (1) : 281-290. ScholarBank@NUS Repository.
Abstract: 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. © 2008 Springer-Verlag.
Source Title: Communications in Mathematical Physics
ISSN: 00103616
DOI: 10.1007/s00220-008-0625-z
Appears in Collections:Staff Publications

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