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arxiv: 2605.13691 · v2 · pith:DNWVA2NFnew · submitted 2026-05-13 · 🪐 quant-ph

Probing Quantum Information Scrambling via Local Randomized Measurements

Yan-Ming Chen , Dan-Bo Zhang This is my paper

Pith reviewed 2026-05-19 17:36 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum information scramblingaveraged accessible informationHaar-random measurementsclassical shadow protocollocal puritymany-body dynamicsrandomized measurementsinformation dynamics
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The pith

Averaged accessible information from Haar-random local measurements equals a function of local purity and reveals scrambling dynamics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to establish that quantum information scrambling can be probed using averaged accessible information extracted from local randomized measurements instead of optimal global ones. It derives an exact analytical relation showing that this averaged accessible information depends only on the purity of the local reduced density matrix when measurements are Haar-random. The classical shadow protocol with single-qubit Pauli measurements then allows practical extraction of this quantity over large subsystems. Simulations across several many-body models demonstrate that the resulting signal distinguishes confinement, ballistic spread, scar revivals, and localization. A reader would care because the method replaces hard-to-implement optimal measurements with accessible local randomness while still capturing essential scrambling features.

Core claim

We derive an analytical expression for the averaged accessible information under Haar-random measurements and show that it is a direct function of the purity of the local reduced density matrix. Using the classical shadow protocol based on single-qubit randomized Pauli measurements, we extract this quantity efficiently across extended subsystems. Numerical simulations in diverse many-body systems then illustrate that the averaged accessible information distinguishes distinct scrambling regimes, including dynamical confinement, ballistic transport, persistent scar revivals, and many-body localization.

What carries the argument

The averaged accessible information (AAI) under Haar-random local measurements, which equals a function of the purity of the local reduced density matrix.

If this is right

  • The averaged accessible information distinguishes dynamical confinement from ballistic transport and from many-body localization.
  • Classical shadow extraction with single-qubit Pauli measurements suffices to obtain the averaged accessible information over extended subsystems.
  • The same quantity captures persistent scar revivals in addition to standard scrambling signals.
  • Randomized local probes replace the need for optimal measurements while still bounding accessible information.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Because averaged accessible information reduces to local purity, time-dependent local purity measurements alone could serve as a practical scrambling diagnostic.
  • The method opens a route to experimental studies of scrambling in systems where optimal measurements are infeasible.
  • Links may exist between this purity-based signal and other local observables already measured in quantum simulators.

Load-bearing premise

The analytical expression for averaged accessible information holds exactly when the measurements are Haar-random on the chosen subsystems and the classical shadow protocol recovers the quantity without significant finite-sample bias.

What would settle it

A large-scale numerical simulation in which the computed averaged accessible information deviates from the value predicted by the local purity function under Haar-random measurements would falsify the central relation.

Figures

Figures reproduced from arXiv: 2605.13691 by Dan-Bo Zhang, Yan-Ming Chen.

Figure 1
Figure 1. Figure 1: FIG. 1. Convergence of AAI ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Spatiotemporal resolution of information scrambling, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Validation of the classical shadow protocol in non-ergodic regimes. The row (a)-(d) compare the exact evolution of the maximal [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dynamical confinement of information in the MBL phase. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

In quantum many-body dynamics, locally encoded information typically scrambles across the entire system, becoming inaccessible to local probes. The upper bound of accessible information of local probes can be characterized by the Holevo information via optimal measurement. In this work, we investigate the information dynamics of quantum scrambling utilizing local randomized probes, quantified by the averaged accessible information (AAI). We derive an analytical expression for the AAI under Haar-random measurements and demonstrate that it is a function of purity of local reduced density matrix. Operationally, we employ the classical shadow protocol, using only single-qubit randomized Pauli measurements, to efficiently extract the AAI across extended subsystems. Through numerical simulations across diverse many-body paradigms, we show that the AAI can reveal distinct scrambling behaviors, resolving phenomena that range from dynamical confinement and ballistic transport to persistent scar revivals and many-body localization. This work highlights a pragmatic paradigm shift--from relying on optimal measurements to utilizing randomized local probes--for the characterization of complex quantum information dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper investigates quantum information scrambling in many-body systems by introducing the averaged accessible information (AAI) extracted from local randomized measurements. The central claims are an analytical derivation showing that the AAI under Haar-random measurements is a function solely of the purity Tr(ρ²) of the local reduced density matrix, an efficient extraction protocol based on single-qubit Pauli classical shadows, and numerical demonstrations that AAI distinguishes scrambling regimes including dynamical confinement, ballistic transport, scar revivals, and many-body localization.

Significance. If the analytical reduction to local purity holds exactly, the work supplies a practical, experimentally accessible probe for scrambling that avoids the need for optimal measurements. The classical-shadow implementation and the numerical illustrations across multiple paradigms add operational value, potentially enabling new diagnostics in quantum simulators.

major comments (2)
  1. [Analytical derivation of AAI] The central claim that the Haar-averaged AAI reduces exactly to a function of Tr(ρ²) alone is load-bearing. The derivation must explicitly demonstrate that all dependence on higher moments of the eigenvalue spectrum of the reduced state cancels after averaging; generic expressions for Holevo information or post-measurement entropy retain spectrum dependence, so the cancellation steps require detailed verification.
  2. [Classical shadow extraction protocol] The classical-shadow protocol section must include a quantitative analysis of bias and variance for finite-shot Pauli measurements when estimating the AAI; without this, it is unclear whether the extracted quantity faithfully reproduces the claimed analytical expression for the system sizes and evolution times considered.
minor comments (2)
  1. [Abstract and § on numerical results] The abstract and introduction should explicitly list the concrete many-body Hamiltonians and initial states used in the numerical benchmarks.
  2. [Figures] Figure captions would benefit from stating the number of disorder realizations, shot counts, and subsystem sizes for each panel to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which will help us improve the clarity and rigor of our presentation. We address each major comment below.

read point-by-point responses

  1. Referee: [Analytical derivation of AAI] The central claim that the Haar-averaged AAI reduces exactly to a function of Tr(ρ²) alone is load-bearing. The derivation must explicitly demonstrate that all dependence on higher moments of the eigenvalue spectrum of the reduced state cancels after averaging; generic expressions for Holevo information or post-measurement entropy retain spectrum dependence, so the cancellation steps require detailed verification.

    Authors: We agree that an expanded presentation of the derivation will strengthen the manuscript. The original derivation shows that the Haar average of the accessible information depends only on the local purity, but we will revise the manuscript to include the intermediate steps explicitly. This will demonstrate how the averaging integrals over the Haar measure cause all higher moments of the eigenvalue spectrum to cancel, leaving dependence solely on Tr(ρ²). The revised version will contain these explicit calculations either in the main text or in a new appendix. revision: yes

  2. Referee: [Classical shadow extraction protocol] The classical-shadow protocol section must include a quantitative analysis of bias and variance for finite-shot Pauli measurements when estimating the AAI; without this, it is unclear whether the extracted quantity faithfully reproduces the claimed analytical expression for the system sizes and evolution times considered.

    Authors: We appreciate the suggestion to quantify the statistical performance of the protocol. In the revised manuscript we will add a dedicated analysis of bias and variance for the finite-shot single-qubit Pauli classical-shadow estimator of the AAI. This will include both analytical error bounds (where tractable) and numerical benchmarks performed at the system sizes and evolution times used in our simulations, confirming that the estimated values reproduce the analytical expression within controlled statistical error. revision: yes

Circularity Check

0 steps flagged

Analytical derivation of AAI as purity function is self-contained with no reduction to inputs

full rationale

The paper states it derives an analytical expression for averaged accessible information (AAI) under Haar-random measurements and shows dependence only on local purity Tr(ρ²). This is presented as a direct calculation from the Holevo quantity averaged over random bases, without evidence that the result is forced by definition, fitted parameters renamed as predictions, or load-bearing self-citations. The subsequent classical shadow protocol is an operational extraction method independent of the analytical claim. No steps reduce by construction to the target result; the derivation chain remains externally verifiable via standard quantum information averaging techniques.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5695 in / 1007 out tokens · 40903 ms · 2026-05-19T17:36:17.243197+00:00 · methodology

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Reference graph

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