## Entangled subspaces and quantum symmetries

### Abstract

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize the entanglement of the subspace, so that a first subspace is more entangled than a second, if the Schmidt string of the second subspace majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.Comment: Latex2e file, 15 page

Topics: Quantum Physics
Publisher: 'American Physical Society (APS)'
Year: 2003
DOI identifier: 10.1103/PhysRevA.69.052331
OAI identifier: oai:arXiv.org:quant-ph/0304132

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