Quantum fidelity for arbitrary Gaussian states

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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.
Original languageEnglish
Article number260501
JournalPhysical Review Letters
Publication statusPublished - 22 Dec 2015

Bibliographical note

Main text (4 pages) plus Appendices


  • quant-ph
  • cond-mat.other
  • math-ph
  • math.MP
  • physics.optics

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