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Universal quantum coding — arXiv:2609.38038

Source

arXiv (en)

Original

https://arxiv.org/abs/2609.38038

License (as archived)

CC0-1.0

Archived

2026-10-07T19:29:22.994Z

SHA-256 of the archived text

35971477f788fb2edb10fce7d608b64ffe0d908eccc06669f2d49fb2dceeb4eb

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https://metraipolis.com/documento/dc_69fe2bc32e65

How to cite

Universal quantum coding — arXiv:2609.38038 — arXiv (en), https://arxiv.org/abs/2609.38038 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_69fe2bc32e65 (Metraipolis archive dc_69fe2bc32e65, sha256 35971477f788fb2edb10fce7d608b64ffe0d908eccc06669f2d49fb2dceeb4eb)

@misc{dc69fe2bc32e65,
  title = {Universal quantum coding — arXiv:2609.38038},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.38038},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_69fe2bc32e65; sha256 35971477f788fb2edb10fce7d608b64ffe0d908eccc06669f2d49fb2dceeb4eb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.38038. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Entanglement distillation from noisy bipartite states and reliable quantum communication over noisy channels are fundamental tasks in quantum information theory, yet optimal coding schemes typically rely on prior knowledge of the underlying state or channel. Here, through Schur-Weyl duality, we establish a universal quantum error-correction principle that removes this dependence entirely. We show that the irreducible permutation spaces arising from the local Schur-Weyl decomposition of many identical copies of an unknown bipartite mixed state form maximally entangled quantum code spaces, with an error structure determined entirely by representation theory. Correcting these symmetry-resolved errors yields universal protocols for entanglement distillation and quantum communication that achieve coherent-information rates with exponentially vanishing error and optimal second-order correction. The protocols are invariant under local unitaries and allow both input marginals to be recovered exactly. At finite block length, their achievable rates are governed by an associated Schur-Weyl information spectrum, which we relate to Petz-Rényi conditional entropies of the underlying state. The resulting sample complexity depends only on the relevant spectral ranks, rather than on the respective Hilbert space dimensions. In particular, for $n$-qubit states of $O(\operatorname{poly} n)$ global rank, we show that a Petz-Rényi conditional-entropy promise suffices for optimal sample-efficient entanglement distillation. Altogether, these results identify Schur-Weyl duality as a fundamental and general mechanism for optimal, tomography-free universal quantum coding, placing entanglement distillation, quantum error correction and quantum communication within a unified representation-theoretic framework.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-30 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.38038 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T18:55:50.628Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).