Comments on Hastings' Additivity Counterexamples
Motohisa Fukuda, Christopher King, David Moser
TL;DR
This paper expands on Hastings' proof of channels violating the additivity conjecture for minimal output entropy, providing detailed explanations and bounds on the dimensions needed for counterexamples.
Contribution
It offers an expanded, detailed version of Hastings' proof and establishes bounds on the minimal dimensions required for counterexamples.
Findings
Hastings' channels violate the additivity conjecture
Bounds on minimal dimensions for counterexamples
Detailed elucidation of Hastings' proof
Abstract
Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the details of the proof, we also present bounds for the minimal dimensions needed to obtain a counterexample.
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