On the Wigner Distribution of the Reduced Density Matrix

• URL: http://arxiv.org/abs/2106.14056v3
• Date: Tue, 15 Nov 2022 19:00:31 GMT
• Title: On the Wigner Distribution of the Reduced Density Matrix
• Authors: Maurice de Gosson and Charlyne de Gosson
• Abstract summary: We show that the Wigner distribution of this reduced density matrix is obtained by integrating the total Wigner distribution with respect to the phase space variables corresponding to subsystem B. Our main result is applied to general Gaussian mixed states, of which it gives a particularly simple and precise description.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: CConsider a bipartite quantum system consisting of two subsystems A and B. The reduced density matrix ofA a is obtained by taking the partial trace with respect to B. In this work, we will show that the Wigner distribution of this reduced density matrix is obtained by integrating the total Wigner distribution with respect to the phase space variables corresponding to subsystem B. The proof we give is rigorous (as opposed to those found in the literature) and makes use of the Weyl--Wigner--Moyal phase space formalism. Our main result is applied to general Gaussian mixed states, of which it gives a particularly simple and precise description. We also briefly discuss the purification of a mixed state from the Wigner formalism point of view.

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