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PreprintarXiv licencearXiv

Distinguishability Transitions from Global Quantum Snapshots

  • Catherine McCarthy
  • Sarang Gopalakrishnan
  • Romain Vasseur
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Abstract

Quantum states generated by generic time evolution are locally featureless: local measurements return random outcomes that are identical for all states. However, global snapshots in the computational basis are surprisingly effective at distinguishing between quantum states. We explore the ability of Bayesian classifiers to discriminate between many random quantum states using a small number of measurement outcomes. We identify a phase transition in the ability of the classifier to distinguish between k candidate states with m shots controlled by the variable x = m / ln k, and derive the threshold value xc. We extend our results to low-depth circuits near the onset of anti-concentration, as well as to noisy circuits and phase-random states.

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Cite

BibTeXRIS
BibTeX
@misc{mccarthy2026distinguishability,
  title = {{Distinguishability Transitions from Global Quantum Snapshots}},
  author = {Catherine McCarthy and Sarang Gopalakrishnan and Romain Vasseur},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09296},
  eprint = {2609.09296},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09296},
}
RIS
TY  - UNPB
TI  - Distinguishability Transitions from Global Quantum Snapshots
AU  - Catherine McCarthy
AU  - Sarang Gopalakrishnan
AU  - Romain Vasseur
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09296
UR  - https://arxiv.org/abs/2609.09296
AB  - Quantum states generated by generic time evolution are locally featureless: local measurements return random outcomes that are identical for all states. However, global snapshots in the computational basis are surprisingly effective at distinguishing between quantum states. We explore the ability of Bayesian classifiers to discriminate between many random quantum states using a small number of measurement outcomes. We identify a phase transition in the ability of the classifier to distinguish between k candidate states with m shots controlled by the variable x = m / ln k, and derive the threshold value x_c. We extend our results to low-depth circuits near the onset of anti-concentration, as well as to noisy circuits and phase-random states.
ER  -