Noise-robust 1-copy distillation protocol for all distillable Bell-diagonal qutrits

TL;DR

This paper presents a noise-robust entanglement distillation protocol for Bell-diagonal qutrits, establishing a clear criterion for 1-distillability based on the PPT condition, and enhancing the practicality of noisy quantum states.

Contribution

It provides a novel, noise-resilient distillation scheme for Bell-diagonal qutrits, solving the longstanding distillability problem for this class of states.

Findings

Violating PPT is necessary and sufficient for 1-distillability of these states.

Constructed a Schmidt rank 2 eigenvector associated with the negative eigenvalue.

Protocol is resilient to white-noise effects, making noisy entangled states more usable.

Abstract

Entanglement distillation is the process of converting noisy entangled states into maximally entangled pure states via local operations and classical communication. A long-standing, unresolved question is which entangled states are amenable to distillation, known as the distillability problem. We solve this for Bell-diagonal qutrits with Weyl structure, and present a noise-robust scheme for entanglement distillation. In particular, we find that violating the positive partial transposition (PPT) criterion is necessary and sufficient for the 1-distillability of these states. For this, we construct a Schmidt rank 2 eigenvector of the partially transposed density matrix associated with its unique, three-fold degenerate negative eigenvalue. This feature makes the derived entanglement distillation protocol resilient to white-noise effects on the quantum states. Our results thus make noisy entangled qutrit pairs more accessible for future quantum technologies.