Quantum fidelity for arbitrary Gaussian states

摘要

We derive a computable analytical formula for the quantum fidelity betweentwo arbitrary multimode Gaussian states which is simply expressed in terms oftheir first- and second-order statistical moments. We also show how such aformula can be written in terms of symplectic invariants and used to deriveclosed forms for a variety of basic quantities and tools, such as the Buresmetric, the quantum Fisher information and various fidelity-based bounds. Ourresult can be used to extend the study of continuous-variable protocols, suchas quantum teleportation and cloning, beyond the current one-mode or two-modeanalyses, and paves the way to solve general problems in quantum metrology andquantum hypothesis testing with arbitrary multimode Gaussian resources.