Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00220-008-0624-0
Title: Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
Authors: Hayden, P.
Winter, A. 
Issue Date: Nov-2008
Citation: Hayden, P., Winter, A. (2008-11). Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1. Communications in Mathematical Physics 284 (1) : 263-280. ScholarBank@NUS Repository. https://doi.org/10.1007/s00220-008-0624-0
Abstract: For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p > 1, the minimum output Rényi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Rényi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors. Since p = 1 corresponds to the von Neumann entropy, these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true, it cannot be proved as a consequence of any channel-independent guarantee of maximal p-norm multiplicativity. We also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2. © 2008 Springer-Verlag.
Source Title: Communications in Mathematical Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/112405
ISSN: 00103616
DOI: 10.1007/s00220-008-0624-0
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