High-Dimensional Carrier-Assisted Entanglement Purification Based on Mutually Unbiased Bases
Abstract
Distilling high-dimensional entanglement under general asymmetric Pauli noise remains challenging. For the unprocessed qutrit single-carrier recurrence studied here, severe noise asymmetry can prevent the convergence condition from being satisfied. In this paper, we investigate carrier-assisted entanglement purification protocols, namely CAEPP and mCAEPP, first for two-qutrit systems, and show that the unprocessed single-carrier recurrence is bottlenecked by marginal X-error probabilities. To overcome this limitation, we introduce MUB-guided preprocessing that combines randomized inversion-pair symmetrization with deterministic maximum-line alignment. For any qutrit Pauli channel with initial fidelity p00>1/3, we prove that, conditioned on successful syndrome outcomes, the MUB-adapted recurrence converges for every sufficiently large fixed carrier number and that its fixed-point fidelity approaches one in the subsequent large-carrier limit. 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 finite-field preprocessing gives the sufficient threshold p00>1/d. A certified equal-target comparison over a finite deterministic optimization domain further shows that neither the MUB-adapted strategy nor complete Pauli-label twirling uniformly dominates the other in finite-resource cost.
Related
- Arbitrary high-dimensional entanglement purification with the superposition of paths
- Mutually unbiased bases as extremal probes of isotropic random Hamiltonians
- More mutually unbiased bases
- Why three? A two-level system with four mutually unbiased questions
- Using topology to reveal all mutually unbiased bases in dimension six
BibTeX
@misc{song2026highdimensional,
title = {{High-Dimensional Carrier-Assisted Entanglement Purification Based on Mutually Unbiased Bases}},
author = {Zihua Song and Lin Chen and Yongge Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.20958},
eprint = {2605.20958},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.20958},
}
RIS
TY - UNPB
TI - High-Dimensional Carrier-Assisted Entanglement Purification Based on Mutually Unbiased Bases
AU - Zihua Song
AU - Lin Chen
AU - Yongge Wang
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2605.20958
UR - https://arxiv.org/abs/2605.20958
AB - Distilling high-dimensional entanglement under general asymmetric Pauli noise remains challenging. For the unprocessed qutrit single-carrier recurrence studied here, severe noise asymmetry can prevent the convergence condition from being satisfied. In this paper, we investigate carrier-assisted entanglement purification protocols, namely CAEPP and mCAEPP, first for two-qutrit systems, and show that the unprocessed single-carrier recurrence is bottlenecked by marginal X-error probabilities. To overcome this limitation, we introduce MUB-guided preprocessing that combines randomized inversion-pair symmetrization with deterministic maximum-line alignment. For any qutrit Pauli channel with initial fidelity p_00>1/3, we prove that, conditioned on successful syndrome outcomes, the MUB-adapted recurrence converges for every sufficiently large fixed carrier number and that its fixed-point fidelity approaches one in the subsequent large-carrier limit. 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 finite-field preprocessing gives the sufficient threshold p_00>1/d. A certified equal-target comparison over a finite deterministic optimization domain further shows that neither the MUB-adapted strategy nor complete Pauli-label twirling uniformly dominates the other in finite-resource cost.
ER -