Normal product form of two-mode Wigner operator.
Sci Rep 2022;
12:2451. [PMID:
35165312 PMCID:
PMC8844086 DOI:
10.1038/s41598-022-06124-8]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 01/24/2022] [Indexed: 11/08/2022] Open
Abstract
In the context of normal product, we use the method of the integration within an ordered product (IWOP) of operators to derive three representations of the two-mode Wigner operator: SU(2) symmetric description, SU(1,1) symmetric description and polar coordinate form. We find that two-mode Wigner operator has multiple potential degrees of freedom. As the physical meaning of the selected integral variable changes, Wigner operator shows different symmetries. In particular, in the case of polar coordinates, we reveal the natural connection between the two-mode Wigner operator and the entangled state representation.
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