Entangled subspaces and quantum symmetries

Journal Article · Sat May 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.052331· OSTI ID:20641144

Bracken, A J ^[1]

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1. Centre for Mathematical Physics, Department of Mathematics, University of Queensland, Brisbane 4072 (Australia)

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 its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second 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.

• OSTI ID: 20641144
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 69; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOUND STATE
CORRELATIONS
ENERGY LEVELS
HILBERT SPACE
HYDROGEN
PROJECTION OPERATORS
QUANTUM MECHANICS
SPIN
SYMMETRY
VECTORS