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Journal of Optics B Quantum and Semiclassical Optics

Bipartite entangled state |$\zeta$$\rangle$ and its applications in quantum communication

Hong-Yi Fan, Mingzhai Sun

Published May 30, 2002• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4266/4/3/311

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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.
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.
Based on the neat ⟨η| representation of the two-mode squeezing operator which entangles signal-mode and idle-mode, where ⟨η| is the common eigenvector of the relative position of two particles and the total momentum exhibiting a maximal entanglement between the two modes, we study some kind of squeezing mixing 1-3 modes and 2-4 modes for a pair of two-mode (1-2 modes and 3-4 modes) squeezed states. The explicit form of such mixed squeezed states is derived and the new entanglement is analysed.