High-Dimensional Carrier-Assisted Entanglement Purification Based on Mutually Unbiased Bases

TL;DR

This paper introduces a novel pre-processing scheme using mutually unbiased bases to enhance high-dimensional entanglement purification, achieving deterministic convergence under asymmetric noise conditions.

Contribution

It proposes a MUB-based deterministic pre-processing method that overcomes convergence bottlenecks in high-dimensional entanglement purification protocols.

Findings

MUB-adapted mCAEPP guarantees unit asymptotic fidelity for certain channels.

Pre-processing based on MUBs effectively manages asymmetric noise.

The approach extends entanglement purification capabilities in high-dimensional quantum systems.

Abstract

Distilling high-dimensional quantum entanglement under realistic, general asymmetric noise remains a formidable challenge. Standard entanglement purification protocols inevitably fail to satisfy convergence constraints under severe asymmetric noise. In this paper, we investigate carrier-assisted entanglement purification protocols, namely CAEPP and mCAEPP, for two-qutrit systems, demonstrating that without adaptive pre-processing, convergence is strictly bottlenecked by marginal $X$-error probabilities. To overcome this limitation, we introduce a deterministic pre-processing scheme based on mutually unbiased bases (MUBs). By actively rotating the qutrit phase space to establish primary-axis error dominance, we rigorously prove that the MUB-adapted mCAEPP deterministically yields unit asymptotic fidelity for any two-qutrit Pauli channel with initial fidelity $p_{00} > 1/3$.