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

arXiv:2605.20958v3 Announce Type: replace 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 $p_{00}>1/3$, 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.

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 $p_{00}>1/3$, 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.

arXiv:2605.20958 [quant-ph]

(or arXiv:2605.20958v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.20958 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

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

Subiecte conexe