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Fully tolerant product state testing and closest product state learning — arXiv:2610.01979

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01979
License (as archived): CC0-1.0
Archived: 2026-10-07T11:38:15.178Z
SHA-256 of the archived text: db14d50c1973d611b05d7e57944921906fa94efaa7de621006ddd5c645b9a6a5
Stable URL of this page: https://metraipolis.com/documento/dc_efd4bdbbe072

How to cite

Fully tolerant product state testing and closest product state learning — arXiv:2610.01979 — arXiv (en), https://arxiv.org/abs/2610.01979 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_efd4bdbbe072 (Metraipolis archive dc_efd4bdbbe072, sha256 db14d50c1973d611b05d7e57944921906fa94efaa7de621006ddd5c645b9a6a5)

BibTeX

@misc{dcefd4bdbbe072,
  title = {Fully tolerant product state testing and closest product state learning — arXiv:2610.01979},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01979},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_efd4bdbbe072; sha256 db14d50c1973d611b05d7e57944921906fa94efaa7de621006ddd5c645b9a6a5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01979. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We address the problem of testing whether an unknown $n$-qudit state $\rho$ is $a$-close to a product state or $b$-far away from any product state, as measured in terms of state overlap. We provide a time-efficient algorithm to solve this problem that requires an $n$-independent number of copies of the unknown state. Our random coloring argument shows that for any unknown state there always exists a partition of $[n]$ into $q$ parts such that the square of the overlap with the closest product state with respect to this partition is only an additive factor $O(1/q)$ larger. This reduces the problem to tolerant testing of $q$ parties, with potentially growing local dimensions. Combining this insight with blockwise spectral projection arguments we can show that the natural $k$-copy generalization of Harrow & Montanaro's product state test provides an efficient tolerant tester. We use the same random coloring and blockwise spectral projection techniques to obtain a substantially improved algorithm for closest product state learning. In particular we give an algorithm that takes in $\widetilde{O}\big((nd)^2\big)\, 2^{\widetilde{O}(1/\varepsilon^8)}$ copies of the unknown state and produces an $\varepsilon$-approximately optimal product state. The key technical components of this learner are a qudit variant of the Bakshi et al. high-fidelity product state learning algorithm and a sampling technique based on Werner's optimal cloning channel.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-02 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.01979 — 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 2026-10-07T11:19:01.728Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).