Divergence-free approach for obtaining decompositions of quantum-optical processes
arXiv:1708.04256 · doi:10.1103/PhysRevA.97.022339
Abstract
Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes contain natural divergences since the maximally entangled state is ill-defined. We introduce a method that avoids such divergences by utilizing finitely entangled (squeezed) states and then taking the limit of arbitrary large squeezing. Using this method we derive an operator-sum representation for all single-mode bosonic Gaussian channels where a unique feature is that both quantum-limited and noisy channels are treated on an equal footing. This technique facilitates a proof that the rank-one Kraus decomposition for Gaussian channels at its respective entanglement-breaking thresholds, obtained in the overcomplete coherent state basis, is unique. The methods could have applications to simulation of continuous-variable channels.
18 pages (8 + appendices), 4 figs. V2: close to published version, dropped Sec.VI of v1 to be expanded elsewhere
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