Generating random Gaussian states
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.
Authors
- Ritabrata Sengupta (ORCID: https://orcid.org/0000-0002-0734-9710)
- Ion Nechita (ORCID: https://orcid.org/0000-0003-3016-7795)
- Leevi Leppäjärvi (ORCID: https://orcid.org/0000-0002-9528-1583)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Toulouse III - Paul Sabatier (FR)
- Université Fédérale de Toulouse Midi-Pyrénées (FR)
- Slovak Academy of Sciences (SK)
- Laboratoire de Physique Théorique (FR)
- Indian Institute of Science Education and Research Berhampur (IN)
- Institute of Physics of the Slovak Academy of Sciences (SK)
Publication Details
- Journal
- Journal of Mathematical Physics
- Published
- 2024-08-01
- DOI
- https://doi.org/10.1063/5.0202147
- Citations
- 2
- Primary Topic
- Quantum Information and Cryptography
- Type
- article
- Field-Weighted Citation Impact
- 0.69
Funders
- Department of Science and Technology, Ministry of Science and Technology, India
- Agence Nationale de la Recherche
- Agentúra na Podporu Výskumu a Vývoja
- Vedecká Grantová Agentúra MŠVVaŠ SR a SAV