Entanglement distillation for continuous-variables under a thermal environment: Effectiveness of a non-Gaussian operation

TL;DR

This paper investigates the effectiveness of non-Gaussian operations for entanglement distillation in continuous-variable systems under thermal noise, comparing strategies applied before or after the noisy channel.

Contribution

It provides a comparative analysis of two distillation strategies, revealing temperature-dependent effectiveness of non-Gaussian operations for entanglement robustness.

Findings

Non-Gaussian operation after noise is more effective at low temperatures.

Non-Gaussian operation before noise is more effective at high temperatures.

Insights into practical entanglement distribution under thermal environments.

Abstract

We study the task of distilling entanglement by a coherent superposition operation $t\hat{a}+r\hat{a}^\dagger$ applied to a continuous-variable state under a thermal noise. In particular, we compare the performances of two different strategies, i.e., the non-Gaussian operation $t\hat{a}+r\hat{a}^\dagger$ is applied before or after the noisy Gaussian channel. This is closely related to a fundamental problem of whether Gaussian or non-Gaussian entanglement can be more robust under a noisy channel and also provides a useful insight into the practical implementation of entanglement distribution for a long-distance quantum communication. We specifically look into two entanglement characteristics, the logarithmic negativity as a measure of entanglement and the teleportation fidelity as a usefulness of entanglement, for each distilled state. We find that the non-Gaussian operation after (before) the thermal noise becomes more effective in the low (high) temperature regime.