Abstract
We show that every Gaussian mixed quantum state can be disentangled by conjugation with a passive symplectic transformation, that is a metaplectic operator associated with a symplectic rotation. The main tools we use are the Werner–Wolf condition on covariance matrices and the symplectic covariance of Weyl quantization. Our result therefore complements a recent study by Lami, Serafini, and Adesso.
Highlights
Gaussian states are important for quantum information processing
Advances in the study of their entanglement properties is useful and of interest to the community working in the area of continuous variable systems which typically get realized in quantum optics
While it is well-known that such states can be made separable (“disentangled”) by diagonalizing the covariance matrix by a symplectic transformation (Williamson normal form), we prove a much stronger result, namely that this disentanglement can.be made by using a symplectic rotation
Summary
Advances in the study of their entanglement properties is useful and of interest to the community working in the area of continuous variable systems which typically get realized in quantum optics. While it is well-known that such states can be made separable (“disentangled”) by diagonalizing the covariance matrix by a symplectic transformation (Williamson normal form), we prove a much stronger result, namely that this disentanglement can.be made by using a symplectic rotation (or “passive symplectic transformation”, to use the physicists’ jargon). We begin by proving the result for bipartite states (Theorem 4), the multipartite readily follows (Corollary 6 ). Theorem 4 has been announced in a Note aux Comptes Rendus de l’Académie des Sciences de Paris [12]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
