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Chinese Physics B

A new approach to obtaining positive-definite Wigner operator for two entangled particles with different masses

范洪义, 徐学翔, Yuan Hong-Chun, Shuai Wang, 王震, 许朋, Nian-Quan Jiang

Published Jul 1, 2011• 4 citations
Publisher

Abstract

Based on our previously proposed Wigner operator in entangled form, we introduce the generalized Wigner operator for two entangled particles with different masses, which is expected to be positive-definite. This approach is able to convert the generalized Wigner operator into a pure state so that the positivity can be ensured. The technique of integration within an ordered product of operators is used in the discussion.

DOI
10.1088/1674-1056/20/7/070301

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Based on our previously proposed Wigner operator in entangled form, we introduce the generalized Wigner operator for two entangled particles with different masses, which is expected to be positive-definite. This approach is able to convert the generalized Wigner operator into a pure state so that the positivity can be ensured. The technique of integration within an ordered product of operators is used in the discussion.
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We introduce a generalized positive-definite operator Δ g (q,p) by smoothing out the Wigner operator Δ w (q,p) and by averaging over the “coarse graining" function. The function is then regarded as the classical Weyl correspondence of the operator Δ g (q,p); in this way we can easily identify a quantum state |Φ〉 such that Δ g (q,p) = |Φ〉 〈Φ|, and |Φ〉 turns out to be a new kind of squeezed coherent state. Correspondingly, the generalized distribution function for any state |Ψ〉 is 〈Ψ|Δ g (q,p)|Ψ〉 = |〈Φ|Ψ〉| 2 , which is obviously positive-definite and is a generalization of the Husimi function.