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Open Systems & Information Dynamics

, Volume 5, Issue 3, pp 209–228 | Cite as

Entropy and Optimal Decompositions of States Relative to a Maximal Commutative Subalgebra

  • Armin Uhlmann
Article

Abstract

To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra is a subfactor.

I consider some general properties, valid for these definitions in finite dimensions, and apply them to a maximal commutative subalgebra of a full matrix algebra. The main method is an interplay between convexity and symmetry. A collection of helpful tools from convex analysis is collected in an appendix.

Keywords

Entropy Statistical Physic Mechanical Engineer System Theory General Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Armin Uhlmann
    • 1
  1. 1.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

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