Please use this identifier to cite or link to this item:
|Title:||Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1|
|Source:||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|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Feb 14, 2018
WEB OF SCIENCETM
checked on Jan 24, 2018
checked on Feb 19, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.