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arXiv:2609.09296

Distinguishability Transitions from Global Quantum Snapshots

Catherine McCarthy, Sarang Gopalakrishnan, Romain Vasseur

cond-mat.stat-mechquant-phSubmitted Sep 8, 2026• Announced Sep 10, 2026• 0 citations
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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 $x_c$. We extend our results to low-depth circuits near the onset of anti-concentration, as well as to noisy circuits and phase-random states.

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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 kkk candidate states with mmm shots controlled by the variable x=m/ln⁡kx = m / \ln kx=m/lnk, and derive the threshold value xcx_cxc​. We extend our results to low-depth circuits near the onset of anti-concentration, as well as to noisy circuits and phase-random states.
We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer ("eavesdropper") can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the eavesdropper has access to. For random unitary circuits with U(1) symmetry, we present an optimal classical classifier to reconstruct the global charge from local measurement outcomes only. We demonstrate the existence of phase transitions in the performance of this classifier in the thermodynamic limit. We also study numerically improved classifiers by including some knowledge about the unitary gates pattern.
Random dynamics in isolated quantum systems is of practical use in quantum information and is of theoretical interest in fundamental physics. Despite a large number of theoretical studies, it has not been addressed how random dynamics can be verified from experimental data. In this paper, based on an information-theoretic formulation of random dynamics, i.e., unitary ttt-designs, we propose a method for verifying random dynamics from the data that is experimentally easy-to-access. More specifically, we use measurement probabilities estimated by a finite number of measurements of quantum states generated by a given random dynamics. Based on a supervised learning method, we construct classifiers of random dynamics and show that the classifiers succeed to characterize random dynamics. We then apply the classifiers to the data set generated by local random circuits (LRCs), which are canonical quantum circuits with growing circuit complexity, and show that the classifiers successfully characterize the growing features. We further apply the classifiers to noisy LRCs, showing the possibility of using them for verifying noisy quantum devices, and to monitored LRCs, indicating that the measurement-induced phase transition may possibly not be directly related to randomness.
Quantum machine learning aims to improve learning methods through the use of quantum computers. If it is to ever realize its potential, many obstacles need to be overcome. A particularly pressing one arises at the prediction stage because the outputs of quantum learning models are inherently random. This creates an often considerable overhead, as many executions of a quantum learning model have to be aggregated to obtain an actual prediction. In this work, we analyze when quantum learning models can evade this issue and produce predictions in a near-deterministic way—paving the way to single-shot quantum machine learning. We give a rigorous definition of single shotness in quantum classifiers and show that the degree to which a quantum learning model is near deterministic is constrained by the distinguishability of the embedded quantum states used in the model. Opening the black box of the embedding, we show that if the embedding is realized by quantum circuits, a certain depth is necessary for single shotness to be even possible. We conclude by showing that quantum learning models cannot be single shot in a generic way and trainable at the same time.
Quantum machine learning aims to improve learning methods through the use of quantum computers. If it is to ever realize its potential, many obstacles need to be overcome. A particularly pressing one arises at the prediction stage because the outputs of quantum learning models are inherently random. This creates an often considerable overhead, as many executions of a quantum learning model have to be aggregated to obtain an actual prediction. In this work, we analyze when quantum learning models can evade this issue and produce predictions in a near-deterministic way -- paving the way to single-shot quantum machine learning. We give a rigorous definition of single-shotness in quantum classifiers and show that the degree to which a quantum learning model is near-deterministic is constrained by the distinguishability of the embedded quantum states used in the model. Opening the black box of the embedding, we show that if the embedding is realized by quantum circuits, a certain depth is necessary for single-shotness to be even possible. We conclude by showing that quantum learning models cannot be single-shot in a generic way and trainable at the same time.
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The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained measurements in the presence of noise. The authors formulate binary quantum classification as constrained quantum state discrimination and introduce a locality-restricted distinguishability measure quantifying the maximum bias achievable by observables acting on at most kkk subsystems. For nnn-qubit systems subject to independent depolarizing noise, the locally accessible signal is governed by a Pauli-weight-dependent contraction mechanism. This motivates a computable predictor, the kkk-local Pauli-accessible amplitude Ak(p)A_{k}(p)Ak​(p), which lower bounds the optimal kkk-local classification advantage. Numerical experiments on four-qubit encodings demonstrate quantitative agreement between empirical accuracy and the prediction across noise levels. The research identifies an operational breakdown threshold where kkk-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.