Qubit Channels Which Require Four Inputs to Achieve Capacity: Implications for Additivity Conjectures

2004/03/31 by Masahito Hayashi, Hiroshi Imai, Keiji Matsumoto +2
Physics and Astronomy · #quant-ph

paper · pdf

published as Quantum Inf. Comput. 5, 13--31 (2005) · 19 pages, 15 figures. several typos corrected in v2

arxiv created 2004/08/26 · arxiv updated 2009/12/01

Abstract

An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and numerical evidence presented which strongly suggests additivity. The numerical evidence also supports a conjecture about the concavity of output entropy as a function of entanglement parameters. However, an example is presented which shows that for some channels this conjecture does not hold for all input states. A numerical algorithm for finding the capacity and optimal inputs is presented and its relation to a relative entropy optimization discussed.

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