Optimizing practical entanglement distillation

TL;DR

This paper introduces numerical and analytical methods to assess and optimize practical entanglement distillation protocols, demonstrating their effectiveness and optimality in various scenarios, including quantum repeater applications.

Contribution

It presents new numerical techniques to compute bounds and improve distillation schemes, along with analytical proofs of optimality for specific protocols.

Findings

Numerical method accurately bounds maximum fidelity for success probability.

Analytical proof of optimality for EPL entanglement protocol.

Numerical optimization can enhance existing distillation schemes.

Abstract

The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a tradeoff between the fidelity to the target state, and the probability of successful distillation. Exploiting such tradeoffs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss (EPL) entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation scheme for a given input state, and we present an example for which this method finds an optimal distillation protocol. An implementation of our numerical methods is available as a Julia package.