title: Quantum Fidelity for Arbitrary Gaussian States.
abstract: We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
authors.affiliation: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
authors.forename: Leonardo
authors.initials: L
authors.lastname: Banchi
authors.affiliation: Computer Science and York Centre for Quantum Technologies, University of York, York YO10 5GH, United Kingdom.
authors.forename: Samuel L
authors.initials: SL
authors.lastname: Braunstein
authors.affiliation: Computer Science and York Centre for Quantum Technologies, University of York, York YO10 5GH, United Kingdom.
authors.forename: Stefano
authors.initials: S
authors.lastname: Pirandola