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arXiv · 1708.04256

Divergence-free approach for obtaining decompositions of quantum-optical processes

K. K. Sabapathy·J. S. Ivan·R. García-Patrón·R. Simon
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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.

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K. K. Sabapathy, J. S. Ivan, R. García-Patrón, R. Simon. 2017-08-14. Divergence-free approach for obtaining decompositions of quantum-optical processes. https://doi.org/10.1103/physreva.97.022339

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