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Refined sample complexities from the tomographic rate function — arXiv:2609.40271

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.40271
License (as archived): CC0-1.0
Archived: 2026-10-07T14:15:22.049Z
SHA-256 of the archived text: 73e43dbcbc1c50b7d58a3b30af9307049b9913ca118d98663675ed44f82eefe4
Stable URL of this page: https://metraipolis.com/documento/dc_ca660ec7904b

How to cite

Refined sample complexities from the tomographic rate function — arXiv:2609.40271 — arXiv (en), https://arxiv.org/abs/2609.40271 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ca660ec7904b (Metraipolis archive dc_ca660ec7904b, sha256 73e43dbcbc1c50b7d58a3b30af9307049b9913ca118d98663675ed44f82eefe4)

BibTeX

@misc{dcca660ec7904b,
  title = {Refined sample complexities from the tomographic rate function — arXiv:2609.40271},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.40271},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ca660ec7904b; sha256 73e43dbcbc1c50b7d58a3b30af9307049b9913ca118d98663675ed44f82eefe4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.40271. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Protocols for quantum state tomography can be characterized either by their sample complexity or by the tomographic rate function that governs the large deviation behaviour of error estimates. We establish a framework for the analysis of covariant protocols which allows us to compare these measures. First, we derive the rate functions for several protocols, including random purification-based protocols and the sample-optimal protocol of Haah et al. These rate functions are expressed in terms of a new family of divergences which includes the reverse sandwiched Rényi divergence and Keyl's annealed quantum relative entropy as special cases. We show that these rate functions obey a strict ordering, even though the sample complexity of each protocol is order optimal. We consider a different version of sample complexity based on Wasserstein distance rather than trace distance, and show that the ordering of the rate functions implies analogous strict inequalities for the Wasserstein-type sample complexity. Thus the tomographic rate function is a more fine-grained indicator of the performance of a tomography protocol than the usual sample complexity.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-01 in math.PR).
Categorie arXiv: Quantum Physics (quant-ph) ; Information Theory (cs.IT); Mathematical Physics (math-ph); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.40271 — 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 2026-10-07T14:04:17.262Z dalla pagina https://arxiv.org/catchup/math.PR/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).