Bargmann invariants of Gaussian states

• URL: http://arxiv.org/abs/2508.07155v1
• Date: Sun, 10 Aug 2025 03:05:53 GMT
• Title: Bargmann invariants of Gaussian states
• Authors: Jianwei Xu,
• Abstract summary: We provide the expression of Bargmann invariant tr($rho _1rho _2...rho _n$) for any $m$-mode bosonic Gaussian states $rho _j_j=1n$.<n>We also use this expression to explore the permissible values of Bargmann invariants for bosonic Gaussian states.
• Score: 0.32634122554914
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Given a set of ordered quantum states, described by density operators $% \{\rho _{j}\}_{j=1}^{n}$, the Bargmann invariant of $\{\rho _{j}\}_{j=1}^{n}$ is defined as tr($\rho _{1}\rho _{2}...\rho _{n}$). 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($\rho _{1}\rho _{2}...\rho _{n}$) for any $m$-mode bosonic Gaussian states $\{\rho _{j}\}_{j=1}^{n}$ in terms of the means and covariance matrices of $\{\rho _{j}\}_{j=1}^{n}.$ We also use this expression to explore the permissible values of Bargmann invariants for bosonic Gaussian states.

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