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Acta Physica Sinica

The physical significances and applications of Schmidt decompositions of continuum bipartile entangled state representation

Fan Hong-Yi, Xuechao Li

Published Jan 1, 2012• 3 citations
Publisher

Abstract

According to the continuum bipartite entangled state representation |η> we derive the Schmidt decomposition of |η>, respectively in the coordinate representation, momentum representation and the particle number representation, and explain their physical significances. As the applications of the Schmidt decomposition, we directly derive the action of the single-mode squeeze operator on |η>, the two-mode squeeze operator's entangled state representation, as well as the matrix element of displacement operator in the Fock space. Generalization of our discussion in this paper to the multipartite entangled state cases is feasible.

DOI
10.7498/aps.61.200301

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Bipartite entangled state |ζ\zetaζ⟩\rangle⟩ and its applications in quantum communication
We analyse the entanglement involved in the common eigenvector | ζ ⟩ of the centre-of-mass coordinate and mass-weighted relative momentum of two particles. Its Schmidt decomposition exhibits that the | ζ ⟩ state maximally entangles two single-mode coordinate (or momentum) eigenstates, of which one is squeezed. The squeezing parameter is related to the ratio of the masses of two particles. The | ζ ⟩ state may describe the entangled state produced by a non-50/50 beamsplitter. Its applications in entanglement swapping and quantum dense coding are discussed. The corresponding entangling operators and swapping operators are derived.
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