Bargmann invariants of Gaussian states

Fuente: arXiv
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Main Author: Xu, Jianwei
Format: Preprint
Published: 2025
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author Xu, Jianwei
author_facet Xu, Jianwei
contents Given a set of ordered quantum states, described by density operators $% \{ρ_{j}\}_{j=1}^{n}$, the Bargmann invariant of $\{ρ_{j}\}_{j=1}^{n}$ is defined as tr($ρ_{1}ρ_{2}...ρ_{n}$). Bargmann invariant serves as a fundamental concept for quantum mechanics and has diverse applications in quantum information science. Bosonic Gaussian states are a class of quantum states on infinite-dimensional Hilbert space, widely used in quantum optics and quantum information science. Bosonic Gaussian states are conveniently and conventionally characterized by their means and covariance matrices. In this work, we provide the expression of Bargmann invariant tr($ρ_{1}ρ_{2}...ρ_{n}$) for any $m$-mode bosonic Gaussian states $\{ρ_{j}\}_{j=1}^{n}$ in terms of the means and covariance matrices of $\{ρ_{j}\}_{j=1}^{n}.$ We also use this expression to explore the permissible values of Bargmann invariants for bosonic Gaussian states.
format Preprint
id arxiv_https___arxiv_org_abs_2508_07155
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Bargmann invariants of Gaussian states
Xu, Jianwei
Quantum Physics
Given a set of ordered quantum states, described by density operators $% \{ρ_{j}\}_{j=1}^{n}$, the Bargmann invariant of $\{ρ_{j}\}_{j=1}^{n}$ is defined as tr($ρ_{1}ρ_{2}...ρ_{n}$). Bargmann invariant serves as a fundamental concept for quantum mechanics and has diverse applications in quantum information science. Bosonic Gaussian states are a class of quantum states on infinite-dimensional Hilbert space, widely used in quantum optics and quantum information science. Bosonic Gaussian states are conveniently and conventionally characterized by their means and covariance matrices. In this work, we provide the expression of Bargmann invariant tr($ρ_{1}ρ_{2}...ρ_{n}$) for any $m$-mode bosonic Gaussian states $\{ρ_{j}\}_{j=1}^{n}$ in terms of the means and covariance matrices of $\{ρ_{j}\}_{j=1}^{n}.$ We also use this expression to explore the permissible values of Bargmann invariants for bosonic Gaussian states.
title Bargmann invariants of Gaussian states
topic Quantum Physics
url https://arxiv.org/abs/2508.07155