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

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, first 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, conditioned on successful syndrome outcomes, the MUB-adapted mCAEPP yields unit asymptotic fidelity for any two-qutrit Pauli channel with initial fidelity $p_{00} > 1/3$. We further extend the algebraic carrier-assisted framework and the asymmetric-noise bottleneck to arbitrary qudit dimensions, and show that in prime-power dimensions the MUB-geometric preprocessing gives the sufficient high-dimensional threshold $p_{00}>(d-1)/(2d)$.