A Novel Stabilizer-based Entanglement Distillation Protocol for Qudits

TL;DR

This paper introduces a stabilizer-based entanglement distillation protocol for qudits that improves fidelity and efficiency, especially for Bell-diagonal states, by analytically linking input states, stabilizers, and protocol properties.

Contribution

It presents a novel two-copy distillation protocol for prime-dimensional bipartite states, demonstrating superior performance over existing methods through analytical and numerical analysis.

Findings

Protocol maximizes fidelity increase per iteration.

Numerical results show improved efficiency and distillability.

Applicable to all bipartite states in prime dimension.

Abstract

Entanglement distillation, the process of converting weakly entangled states into maximally entangled ones using Local Operations and Classical Communication (LOCC), is pivotal for robust entanglement-assisted quantum information processing in error-prone environments. A construction based on stabilizer codes offers an effective method for designing such protocols. By analytically investigating the effective action of stabilizer protocols for systems of prime dimension $d$, we establish a standard form for the output states of recurrent stabilizer-based distillation. This links the properties of input states, stabilizers, and encodings to the properties of the protocol. Based on those insights, we present a novel two-copy distillation protocol, applicable to all bipartite states in prime dimension, that maximizes the fidelity increase per iteration for Bell-diagonal states. The power of this framework and the protocol is demonstrated through numerical investigations, which provide evidence for superior performance in terms of efficiency and distillability of low-fidelity states compared to other well-established recurrence protocols. By elucidating the interplay between states, errors, and protocols, our contribution advances the systematic development of highly effective distillation protocols, enhancing our understanding of distillability.