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

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

2004-03-24

arxiv.org/abs/quant-ph/0403176v2

Quantum Inf. Comput. 5, 13--31 (2005)

Physics

Quantum Physics

19 pages, 15 figures. several typos corrected in v2

Scientific paper

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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