Efficient entanglement purification protocols for d-level systems

TL;DR

This paper presents new entanglement purification protocols for d-level quantum systems (qudits) that are more efficient and robust than previous methods, with potential advantages for long-distance quantum communication.

Contribution

The authors develop and analyze improved entanglement purification protocols for qudits, including recurrence and hashing schemes, with enhanced efficiency and noise robustness compared to prior work.

Findings

Protocols outperform previous approaches in efficiency and robustness.

Performance improves with increasing local dimension.

Protocols are suitable for long-distance quantum communication.

Abstract

We introduce entanglement purification protocols for d-level systems (qudits) with improved efficiency as compared to previous protocols. While we focus on protocols for bipartite systems, we also propose generalizations to multi-partite qudit systems. The schemes we introduce include recurrence protocols that operate on two copies, as well as hashing protocols that operate on large ensembles. We analyze properties of the protocols with respect to minimal required fidelity and yield, and study their performance in the presence of noise and imperfections. We determine error thresholds and study the dependence on local dimension. We find that our schemes do not only outperform previous approaches, but also show an improved robustness and better efficiency with increasing dimension. While error thresholds for different system sizes are not directly comparable, our results nevertheless suggest that quantum information processing using qudits, in particular for long-distance quantum communication, may offer an advantage over approaches based on qubit systems.