Strategies for enhancing quantum entanglement by local photon subtraction

TL;DR

This paper analyzes various local photon subtraction strategies on two-mode squeezed states, considering imperfections and losses, to optimize entanglement gain and success probability for quantum communication applications.

Contribution

It develops a comprehensive framework incorporating losses and imperfections, comparing symmetric and asymmetric subtraction strategies, and identifying optimal parameters for entanglement enhancement.

Findings

Single-photon subtraction from one mode yields maximum entanglement gain in lossless conditions.

Losses significantly influence the optimal subtraction strategy, requiring tailored approaches.

Asymmetric subtraction can outperform symmetric strategies under certain lossy conditions.

Abstract

Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyse different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimised set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximise the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.