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Entangled state for constructing a generalized phase-space representation and its statistical behavior

2009; American Physical Society; Volume: 80; Issue: 2 Linguagem: Inglês

10.1103/physreva.80.022115

1538-4446

Li-Yun Hu, Hong-Yi Fan,

Quantum Information and Cryptography

We construct a generalized phase-space representation (GPSR) based on the idea of Einstein-Podolsky-Rosen quantum entanglement, i.e., we generalize the Torres-Vega-Frederick phase-space representation to the entangled case, which is characteristic of the features when two particles' relative coordinate, total momentum operators, and their conjugative variables, respectively, operate on the GPSR. This representation is complete and nonorthogonal. The Weyl-ordered form of the density operator of GPSR is derived, and its identification with the generalized Husimi operator is recognized, which clearly exhibit its statistical behavior. The minimum uncertainty relation obeyed by the GPSR is also demonstrated.