Generating random Gaussian states

• URL: http://arxiv.org/abs/2401.13435v1
• Date: Wed, 24 Jan 2024 13:06:57 GMT
• Title: Generating random Gaussian states
• Authors: Leevi Lepp\"aj\"arvi, Ion Nechita, Ritabrata Sengupta
• Abstract summary: We show that the eigenvalues of an RQCM converge to a shifted semicircular distribution in the limit of a large number of modes. We show that the symplectic eigenvalues of an RQCM converge to a probability distribution that can be characterized using free probability.
• Score: 0.4604003661048266
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a method for the random sampling of (multimode) Gaussian states in terms of their covariance matrix, which we refer to as a random quantum covariance matrix (RQCM). We analyze the distribution of marginals and demonstrate that the eigenvalues of an RQCM converge to a shifted semicircular distribution in the limit of a large number of modes. We provide insights into the entanglement of such states based on the positive partial transpose (PPT) criteria. Additionally, we show that the symplectic eigenvalues of an RQCM converge to a probability distribution that can be characterized using free probability. We present numerical estimates for the probability of a RQCM being separable and, if not, its extendibility degree, for various parameter values and mode bipartitions.

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