Abstract
For entangled three particles one should treat their wave function as a whole. There is no physical meaning talking about the wave function (or Wigner function) for any one of the tripartite, and therefore considering the entangled Wigner function (Wigner operator) is of necessity. In this paper, we introduce a pair of mutually conjugate tripartite entangled state representations for defining the Wigner operator of entangled tripartite. Its marginal distributions and the Wigner function of the three-mode squeezed vacuum state are presented. Deriving wave function from its corresponding tripartite entangled Wigner function is also discussed. Moreover, through establishing the n-mode entangled state representation, we introduce the n-mode entangled Wigner operator, which would be more generally useful in quantum physics.
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