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Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination — arXiv:2609.40355

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.40355
License (as archived): CC0-1.0
Archived: 2026-10-07T15:22:44.229Z
SHA-256 of the archived text: b7571f5bd2b1ffb836ea8fdc73b4a872f388efe0372c019204e7d2ced59950e1
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How to cite

Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination — arXiv:2609.40355 — arXiv (en), https://arxiv.org/abs/2609.40355 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_85412fe72dfd (Metraipolis archive dc_85412fe72dfd, sha256 b7571f5bd2b1ffb836ea8fdc73b4a872f388efe0372c019204e7d2ced59950e1)

BibTeX

@misc{dc85412fe72dfd,
  title = {Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination — arXiv:2609.40355},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.40355},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_85412fe72dfd; sha256 b7571f5bd2b1ffb836ea8fdc73b4a872f388efe0372c019204e7d2ced59950e1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.40355. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Given multiple uses of an unknown quantum channel, we determine whether it is a specified non-mixed-unitary channel or belongs to the set of mixed-unitary channels. Formulating this as a composite channel hypothesis testing problem, we characterize the Stein exponents achievable by parallel strategies under progressively weaker restrictions on probe states and auxiliary memory. In particular, we consider block-i.i.d. probes, which allow arbitrary correlations within blocks of fixed size while remaining i.i.d. across different blocks, and derive finite-letter expressions of the corresponding Stein exponents. Varying the block size, which interpolates between fully i.i.d. and arbitrary probes, together with further restrictions on intra-block correlations and access to auxiliary memory, results in a multifaceted hierarchy. We establish several strict separations within this hierarchy. Without auxiliary memory, we prove that fully i.i.d. probes yield a vanishing Stein exponent for every unital non-mixed-unitary channel, while blocks of three product probes suffice to obtain a strictly positive exponent for the qutrit Werner-Holevo channel. For block size two, although product probes seem to be insufficient for $O(3)$-covariant channels, an entangled probe achieves a strictly positive exponent for the qutrit Werner-Holevo channel, even though every maximally entangled probe fails. In contrast, access to auxiliary memory makes fully i.i.d. probes sufficient by yielding a strictly positive exponent for every non-mixed-unitary channel, even without requiring input-reference entanglement, and this exponent admits a lower bound determined by the diamond-norm distance from the mixed-unitary set. Moreover, for odd-dimensional Werner-Holevo channels, we find that this exponent is infinite, with every full-Schmidt-rank pure state being optimal.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-01 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.40355 — 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 2026-10-07T14:53:56.906Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).