Optimal Interpolation of Entanglement Purification Protocols

TL;DR

This paper develops an optimal method for selecting entanglement purification protocols to maximize the rate and fidelity of Bell pairs produced, considering both asymptotic and finite-size scenarios.

Contribution

It introduces a strategy to choose protocol distributions that optimize entanglement purification performance beyond individual protocols.

Findings

Maximized the rate of producing high-fidelity Bell pairs.

Achieved higher fidelities at given rates through protocol mixing.

Provided analysis for both infinite and finite initial pairs.

Abstract

Bipartite entanglement purification is the conversion of copies of weakly entangled pairs shared between two separated parties into a smaller number of strongly entangled shared pairs using only local operations and classical communication. Choosing between different entanglement purification protocols generally involves weighing up a trade-off between the ratio of strongly entangled pairs produced to weakly entangled pairs consumed, which we call the rate of the protocol, and the degree of the entanglement of the strongly entangled pairs, typically measured by the fidelity of those pairs to maximally entangled states. By randomly choosing a protocol according to a probability distribution over a list of protocols for each pair we want to produce, we can achieve rates and fidelities not achieved by any of the original protocols. Here, we show how to choose this distribution to maximise the rate at which we produce qubit pairs with a given fidelity to a Bell state or, equivalently, to maximise the fidelity to a Bell state of the qubit pairs produced at a given rate. We investigate both the asymptotic case, where the number of initial pairs goes to infinity, and the finite-size regime, where protocols are restricted to a finite number of weakly entangled pairs.