Qubit channels which require four inputs to achieve capacity: implications for additivity conjectures

Authors:
Masahito Hayashi;Hiroshi Imai;Keiji Matsumoto;Mary Beth Ruskai;Toshiyuki Shimono
Affiliations:
ERATO Quantum Computation and Information Project, JST, Hongo, Bunkyo-ku, Tokyo, Japan;Department of Computer Science, The University of Tokyo, Tokyo, Japan and ERATO Quantum Computation and Information Project, JST, Hongo, Bunkyo-ku, Tokyo, Japan;ERATO Quantum Computation and Information Project, JST, Hongo, Bunkyo-ku, Tokyo, Japan and National Institute of Informatics (NII), Tokyo, Japan;Department of Mathematics, Tufts University, Medford, Massachusetts;Department of Computer Science, The University of Tokyo, Tokyo, Japan
Venue:
Quantum Information & Computation
Year:
2005

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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.