A Caltech Library Service

On Hastings' Counterexamples to the Minimum Output Entropy Additivity Conjecture

Brandão, Fernando G. S. L. and Horodecki, Michał (2010) On Hastings' Counterexamples to the Minimum Output Entropy Additivity Conjecture. Open Systems & Information Dynamics, 17 (1). pp. 31-52. ISSN 1230-1612. doi:10.1142/S1230161210000047.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.

Item Type:Article
Related URLs:
URLURL TypeDescription
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2010 World Scientific Publishing. Received: August 13, 2009.
Issue or Number:1
Record Number:CaltechAUTHORS:20160523-163304954
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67272
Deposited By: Joy Painter
Deposited On:24 May 2016 00:07
Last Modified:11 Nov 2021 00:29

Repository Staff Only: item control page