Operator transpose within normal ordering and its applications for quantifying entanglement

• URL: http://arxiv.org/abs/2103.07821v1
• Date: Sun, 14 Mar 2021 00:34:39 GMT
• Title: Operator transpose within normal ordering and its applications for quantifying entanglement
• Authors: Liyun Hu, Luping Zhang, Xiaoting Chen, Wei Ye, Qin Guo, and Hongyi Fan
• Abstract summary: We study the (partial) transpose of any single (two-mode) operators. It is found that the transposed operator of an arbitrary operator can be obtained by replacement of adag(a) by a(adag) instead of c-number.
• Score: 3.519220831057493
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary operator can be obtained by replacement of a^{{\dag}}(a) by a(a^{{\dag}}) instead of c-number within normal ordering form. The transpose of displacement operator and Wigner operator are studied, from which the relation of Wigner function, characteristics function and average values such as covariance matrix are constructed between density operator and transposed density operator. These observations can be further extended to multi-mode cases. As applications, the partial transpose of two-mode squeezed operator and the entanglement of two-mode squeezed vacuum through a laser channel are considered.

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