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

TL;DR

This paper introduces a divergence-free method using finitely entangled states to derive operator-sum representations of quantum channels, specifically for continuous-variable systems, enabling a unified treatment of quantum-limited and noisy channels.

Contribution

It presents a novel approach that avoids divergences in continuous-variable quantum channel representations by employing finitely entangled states and taking limits, providing a unified framework.

Findings

Derived operator-sum representations for all single-mode bosonic Gaussian channels.

Proved the uniqueness of the rank-one Kraus decomposition at entanglement-breaking thresholds.

Facilitated potential applications in simulating continuous-variable quantum channels.

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.