dorsal/arxiv
View SchemaEntropy and optimal decompositions of states relative to a maximal commutative subalgebra
| Authors | Armin Uhlmann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9704017 |
| URL | https://arxiv.org/abs/quant-ph/9704017 |
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 for the problems in question is collected in an appendix.
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"abstract": "To calculate the entropy of a subalgebra or of a channel with respect to a\nstate, one has to solve an intriguing optimalization problem. The latter is\nalso the key part in the entanglement of formation concept, in which case the\nsubalgebra is a subfactor. I consider some general properties, valid for these\ndefinitions in finite dimensions, and apply them to a maximal commutative\nsubalgebra of a full matrix algebra. The main method is an interplay between\nconvexity and symmetry. A collection of helpful tools from convex analysis for\nthe problems in question is collected in an appendix.",
"arxiv_id": "quant-ph/9704017",
"authors": [
"Armin Uhlmann"
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"title": "Entropy and optimal decompositions of states relative to a maximal commutative subalgebra",
"url": "https://arxiv.org/abs/quant-ph/9704017"
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