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Robustness of quantum spectrum estimation: weak Schur sampling under noisy inputs — arXiv:2610.03582

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arXiv (en)

Original

https://arxiv.org/abs/2610.03582

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CC0-1.0

Archived

2026-10-06T08:40:48.566Z

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Robustness of quantum spectrum estimation: weak Schur sampling under noisy inputs — arXiv:2610.03582 — arXiv (en), https://arxiv.org/abs/2610.03582 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2744b5a135ca (Metraipolis archive dc_2744b5a135ca, sha256 c40a76e38e70dbe83f3af9cbd3180b63aeaf25fd73c1fd05419a28adcfa4d2a7)

@misc{dc2744b5a135ca,
  title = {Robustness of quantum spectrum estimation: weak Schur sampling under noisy inputs — arXiv:2610.03582},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.03582},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2744b5a135ca; sha256 c40a76e38e70dbe83f3af9cbd3180b63aeaf25fd73c1fd05419a28adcfa4d2a7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.03582. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We initiate the study of weak Schur sampling (WSS) under noisy inputs. Many optimal quantum learning algorithms rely on this measurement, for instance in quantum spectrum estimation (QSE) and quantum state tomography (QST). The standard analysis of WSS, QSE and QST assumes that the $n$ input copies of the target state $\rho$ are identical, i.e. $\rho^{\otimes n}$. We study what happens when they are not, a more realistic noisy scenario that breaks the very permutation symmetry on which WSS is built. In the simplest model the input is a noisy product state: the copies are independent but not necessarily identical and each is $\epsilon$-close in trace distance to the $d$-dimensional target state $\rho$. A naive argument via the data-processing inequality allows the per-copy errors to accumulate to $n\epsilon$ on the measurement outcome. We show that for QSE via WSS this does not happen: the expected estimation error in total variation is at most $\epsilon+\eta(n,d)$, where $\eta(n,d)=O(d/\sqrt n)$ is the noiseless error, and the additive noise term $\epsilon$ is optimal. The output error does not grow with $n$ even though the input error does; in this sense WSS is robust. Beyond noisy product states, for arbitrary input $\omega$ we show that the error is at most $\eta(n,d)+\frac{1}{n}\|\omega-\rho^{\otimes n}\|_{W_1}$, where $W_1$ is the quantum Wasserstein distance of De Palma et al. In particular, our results imply, for the first time, noise-robustness of Keyl and Werner's seminal algorithm for QSE, more than two decades after its introduction. Finally, we show that the noise cannot be too bad: within our model of robustness the promise on the input cannot be weakened to closeness of single-copy marginals or to a global trace-distance budget alone, as in both cases some inputs defeat every measurement and estimator.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-05 in math.IT).
Categorie arXiv: Quantum Physics (quant-ph) ; Information Theory (cs.IT); Representation Theory (math.RT).
Pagina del lavoro: https://arxiv.org/abs/2610.03582 — 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 2026-10-06T08:19:47.074Z dalla pagina https://arxiv.org/catchup/math.IT/2026-10-05?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).