A Novel Stabilizer-based Entanglement Distillation Protocol for Qudits

Christopher Popp; Tobias C. Sutter; Beatrix C. Hiesmayr

doi:10.22331/q-2025-12-15-1945

A Novel Stabilizer-based Entanglement Distillation Protocol for Qudits

Christopher Popp, Tobias C. Sutter, and Beatrix C. Hiesmayr

University of Vienna, Faculty of Physics, Währingerstrasse 17, 1090 Vienna.

Published:	2025-12-15, volume 9, page 1945
Editor:	Remigiusz Augusiak
Eprint:	arXiv:2408.02383v3
Doi:	https://doi.org/10.22331/q-2025-12-15-1945
Citation:	Quantum 9, 1945 (2025).

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Abstract

Entanglement distillation, the process of converting weakly entangled states into maximally entangled ones using Local Operations and Classical Communication (LOCC), is pivotal for robust entanglement-assisted quantum information processing in error-prone environments. A construction based on stabilizer codes offers an effective method for designing such protocols. By analytically investigating the effective action of stabilizer protocols for systems of prime dimension $d$, we establish a standard form for the output states of recurrent stabilizer-based distillation. This links the properties of input states, stabilizers, and encodings to the properties of the protocol. Based on those insights, we present a novel two-copy distillation protocol, applicable to all bipartite states in prime dimension, that maximizes the fidelity increase per iteration for Bell-diagonal states. The power of this framework and the protocol is demonstrated through numerical investigations, which provide evidence for superior performance in terms of efficiency and distillability of low-fidelity states compared to other well-established recurrence protocols. By elucidating the interplay between states, errors, and protocols, our contribution advances the systematic development of highly effective distillation protocols, enhancing our understanding of distillability.

Popular summary

Entanglement is a remarkable feature of quantum mechanics, allowing particles to share correlations beyond classical physics. These correlations underpin quantum communication, computing, and sensing, but in practice entanglement is fragile: noise quickly degrades it. To counter this, we use entanglement distillation, which converts several weak or noisy states into fewer, less noisy, and thereby more usable ones.
In this study, we introduce a new distillation method for qudits—quantum systems with two or more levels. Using stabilizer codes, a framework from quantum error correction, we establish a systematic way to describe how stabilizer-based protocols act on imperfect states. Building on this foundation, we propose a two-copy protocol that applies to all states in prime dimensions and achieves the maximum possible improvement in each round for noise-affected Bell states. Our simulations show that the method outperforms established protocols, especially for high levels of noise.
By clarifying the link between input states, stabilizers, and outcomes, we advance efficient distillation strategies and strengthen the foundation for robust quantum networks and scalable quantum technology.

► BibTeX data

@article{Popp2025novelstabilizer,
  doi = {10.22331/q-2025-12-15-1945},
  url = {https://doi.org/10.22331/q-2025-12-15-1945},
  title = {A {N}ovel {S}tabilizer-based {E}ntanglement {D}istillation {P}rotocol for {Q}udits},
  author = {Popp, Christopher and Sutter, Tobias C. and Hiesmayr, Beatrix C.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1945},
  month = dec,
  year = {2025}
}

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Cited by

[1] Christopher Popp, Tobias C. Sutter, and Beatrix C. Hiesmayr, "Resource state distillation via stabilizer channels", Physical Review A 114 1, 012421 (2026).

[2] Tobias C. Sutter, Christopher Popp, and Beatrix C. Hiesmayr, "Group-theoretic perspective on the positive-partial-transpose and realignment criteria in the magic simplex for bipartite qutrits", Physical Review A 113 3, 032440 (2026).

[3] Jacky Jiang, Natalie Klco, and Olivia Di Matteo, "Non-Abelian dynamics on a cube: Improving quantum compilation through qudit-based simulations", Physical Review D 112 7, 074512 (2025).

[4] Karol Horodecki, Marek Winczewski, Leonard Sikorski, Paweł Mazurek, Mikołaj Czechlewski, and Raja Yehia, "Quantification of the energy consumption of entanglement distribution", arXiv:2507.23108, (2025).

[5] Christopher Popp, Tobias C. Sutter, and Beatrix C. Hiesmayr, "Low-fidelity entanglement distillation with FIMAX", International Journal of Quantum Information 23 6, 2550017 (2025).

[6] Dariusz Chruściński, Anindita Bera, Joonwoo Bae, and Beatrix C. Hiesmayr, "A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist", arXiv:2503.04158, (2025).

[7] Tobias C. Sutter, Christopher Popp, and Beatrix C. Hiesmayr, "Noise-robust 1-copy distillation protocol for all distillable Bell-diagonal qutrits", arXiv:2604.24460, (2026).

[8] Dariusz Chruściński, Anindita Bera, Joonwoo Bae, and Beatrix C. Hiesmayr, "A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist", Scientific Reports 15 1, 28205 (2025).

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