Fidelity for multimode thermal squeezed states
Gheorghe Sorin Paraoanu, Horia Scutaru · Physical Review A · 2000
In the theory of quantum transmission of information the concept of fidelity plays a fundamental role. An important class of channels, which can be experimentally realized in quantum optics, is that of Gaussian quantum channels. In this work we present a general formula for fidelity in the case of two arbitrary Gaussian states. From this formula one can get a previous result [H. Scutaru, J. Phys. A 31, 3659 (1998)], for the case of a single mode. The concept of fidelity used in this paper is the standard one [D. Bures, Trans. Am. Math. Soc. 135, 199 (1969); A. Uhlmann, Rep. Math. Phys. 9, 273 (1976); R. Josza, J. Mod. Opt. 41, 2314 (1994)]. It can be defined by $F({\ensuremath{\rho}}_{1},{\ensuremath{\rho}}_{2}{)}^{\underset{=}{\mathrm{def}}}{\mathrm{max}}_{|{\ensuremath{\psi}}_{1}〉,|{\ensuremath{\psi}}_{2}〉}|〈{\ensuremath{\psi}}_{1}|{\ensuremath{\psi}}_{2}〉{|}^{2},$ where $|{\ensuremath{\psi}}_{i}〉,$ $i=1,2$ are purifications of the density matrices ${\ensuremath{\rho}}_{i}.$