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Coherent states, entanglement, and geometric invariant theory
Alexander Klyachko
abstract: The main objective of the paper is to unveil an adequate mathematics hidden
behind entanglement, that is Geometric Invariant Theory. More specifically
relation between these two subjects can be described by the following theses.
(i) Total variance of completely entangled state is maximal. (ii) This
distinguishes the state as a minimal vector in its orbit under action of
complexified dynamic group.
(iii) An ultimate aim of Geometric Invariant Theory is a description of
complex orbits and their minimal vectors. It suggests that noncompletely
entangled states are just GIT semistable vectors.
- oai_identifier:
- oai:arXiv.org:quant-ph/0206012
- categories:
- quant-ph
- comments:
- 19 pages
- arxiv_id:
- quant-ph/0206012
- created:
- 2002-06-03
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