Year: 2024
Type: article
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 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.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0202147
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1354815760, G1417945601, Slovak Academic and Scientific PROgramme for experienced researchers, G1630729474, Navrhovanie kvantových štruktúr vyššieho rádu, G2229715109, Stochastic Quantum Evolutions, G3259454348, Dizajn zložitých kvantových meraní (DESCOM), G4246281229, G434337789, Space of Traffics and Asymptotics of Random Spectra, G4997507351, G6268741103, G7664169557, G8347671446
OpenAlex ID: W4401548846