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arxiv: 2607.02462 · v1 · pith:YOS4UMEBnew · submitted 2026-07-02 · 🪐 quant-ph · cond-mat.stat-mech· cond-mat.str-el

Quantum mutual information as a robust probe of integrability in open quantum systems

Nirupam Sen , Keshav Das Agarwal , Aditi Sen De This is my paper

Pith reviewed 2026-07-03 11:31 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechcond-mat.str-el
keywords integrabilitychaosquantum scramblingmutual informationopen quantum systemsMarkovian dynamicsnon-Markovian dynamicsXYZ model
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The pith

The temporal fluctuations of the averaged sum of total correlations distinguish integrable from chaotic dynamics in open quantum systems.

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

The paper develops an information-theoretic approach using the Haar-averaged sum of total correlations to detect whether the dynamics of a quantum system arise from an integrable or chaotic Hamiltonian. It demonstrates that the long-time average and particularly the fluctuations of this quantity provide a reliable, system-size-independent indicator, akin to out-of-time-ordered correlators. In open systems coupled to a thermal bath, these fluctuations maintain their ability to differentiate the regimes at intermediate times for Markovian dynamics and at long times when non-Markovian effects allow information backflow. The approach also succeeds in certain weak noise regimes where the standard scrambling measure fails.

Core claim

Using the long-range quantum XYZ spin model with an integrable limit given by the nearest-neighbor transverse XY model, the long-time average and temporal fluctuations of the aSTC, defined as the Haar-averaged sum of total correlations, serve as faithful signatures of integrable versus chaotic dynamics. This signature remains effective in the presence of system-bath coupling, with non-Markovian dynamics restoring the distinction at long times through information backflow, and under specific Markovian and non-Markovian noises where it outperforms the OTOC.

What carries the argument

The Haar-averaged sum of total correlations (aSTC), which measures the average quantum mutual information generated from initially separable states across all partitions.

If this is right

  • The distinction via aSTC fluctuations holds independently of system size in closed systems.
  • In Markovian open quantum systems, the distinguishing power is limited to intermediate times.
  • Non-Markovian information backflow extends the utility of aSTC to long times.
  • Under weak Markovian amplitude damping, aSTC fluctuations can identify integrability even when OTOC cannot.

Where Pith is reading between the lines

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

  • The method may apply to experimental platforms with controllable noise to study many-body integrability.
  • Since it relies on mutual information, it could connect to other entanglement-based diagnostics in open systems.
  • Testing in models beyond the XYZ family would confirm the generality of the probe.

Load-bearing premise

The qualitative distinction observed in the long-range XYZ model generalizes to other systems with integrable-to-chaotic transitions.

What would settle it

Observing whether the temporal fluctuations of aSTC fail to separate integrable and chaotic regimes in a different model, such as the Ising chain with transverse field, at long times in closed systems.

Figures

Figures reproduced from arXiv: 2607.02462 by Aditi Sen De, Keshav Das Agarwal, Nirupam Sen.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a)). This decay reflects a fundamental competition between internal system interactions and environmental dis￾sipation [78], where the baths suppress the mutual informa￾tion created among the initial product states. As the system￾bath coupling γ (z) increases, the STC decays more rapidly, suppressing both its late-time mean value and its temporal fluctuations. Nevertheless, in the weak-coupling regime, th… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
read the original abstract

The dynamics of a quantum system encode signatures of whether the underlying Hamiltonian is integrable or chaotic, giving rise to the concept of quantum information scrambling through the properties of the resulting dynamical states or operators. We introduce an information-theoretic framework based on the Haar-averaged sum of total correlations (aSTC), together with average genuine multipartite entanglement generated dynamically from initially fully separable states, as robust probes of quantum information scrambling. Using the long-range quantum XYZ spin model in transverse and longitudinal magnetic fields, whose integrable limit is the nearest-neighbor transverse XY model, we demonstrate that the long-time average and, more importantly, the temporal fluctuations of the aSTC provide a faithful and system-size-independent signature of integrable and chaotic dynamics, similar to the conventional measure of scrambling, out-of-time-ordered correlator (OTOC). When the system is in contact with the thermal reservoir and system-bath coupling follows Markovianity, we find that the fluctuations of the aSTC and OTOC continue to distinguish integrable and chaotic dynamics only at intermediate times. However, we observe that in the non-Markovian domain, information backflow restores the scrambling dynamics, enabling the aSTC to retain its distinguishing power even at long times. Interestingly, we exhibit that, under Markovian amplitude damping and non-Markovian dephasing noise, the temporal fluctuations of the aSTC can discriminate between integrability and non-integrability in the weak Markovian regime, even when OTOC fails to do so.

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 / 1 minor

Summary. The manuscript introduces the Haar-averaged sum of total correlations (aSTC), based on quantum mutual information, and average genuine multipartite entanglement as information-theoretic probes of scrambling and integrability. Using numerical simulations on the long-range quantum XYZ spin model (whose integrable point is the nearest-neighbor transverse XY model), it claims that the long-time average and temporal fluctuations of aSTC distinguish integrable from chaotic dynamics in a system-size-independent way, comparable to the out-of-time-ordered correlator (OTOC). In open systems coupled to thermal baths, the work examines Markovian and non-Markovian regimes and reports that aSTC fluctuations retain distinguishing power at long times in the non-Markovian case and can succeed under certain weak Markovian noise channels where OTOC fails.

Significance. If the numerical results hold under scrutiny, the work supplies a potentially practical alternative to OTOC for diagnosing integrability and scrambling that appears more robust to dissipation and information backflow. The focus on temporal fluctuations rather than solely averages, together with the reported system-size independence, would be a useful addition to the toolkit for open quantum systems if the supporting evidence is made fully reproducible.

major comments (2)
  1. [Abstract] The central claim that aSTC fluctuations furnish a 'faithful and system-size-independent signature of integrable and chaotic dynamics' (abstract) rests exclusively on demonstrations within the long-range XYZ family. No other integrable-to-chaotic transitions (e.g., XXZ chain or Floquet models) are examined, so the reported distinction and size independence may be specific to the chosen long-range interactions or the particular crossover rather than a general feature of the measure.
  2. [Abstract] The abstract asserts numerical demonstrations of system-size independence and distinguishing power of long-time averages and fluctuations, yet provides no information on the range of system sizes examined, the presence or absence of error bars, the precise definition of the long-time window, or the numerical procedure for the Haar average. These omissions prevent verification that the reported behavior is not an artifact of post-hoc choices or finite-size effects.
minor comments (1)
  1. [Title/Abstract] The title emphasizes 'quantum mutual information' while the abstract centers on the derived quantity aSTC; a short clarifying sentence relating the two would improve accessibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. Below we provide a point-by-point response to the major comments and indicate the changes we will implement.

read point-by-point responses

  1. Referee: [Abstract] The central claim that aSTC fluctuations furnish a 'faithful and system-size-independent signature of integrable and chaotic dynamics' (abstract) rests exclusively on demonstrations within the long-range XYZ family. No other integrable-to-chaotic transitions (e.g., XXZ chain or Floquet models) are examined, so the reported distinction and size independence may be specific to the chosen long-range interactions or the particular crossover rather than a general feature of the measure.

    Authors: We acknowledge that all numerical results are obtained within the long-range XYZ family, selected because it possesses a well-defined integrable limit (nearest-neighbor transverse XY model) while allowing tunable long-range interactions. The abstract phrasing is therefore tied to this concrete setting rather than asserted as universal. To prevent overgeneralization we will revise the abstract to state that the signatures are demonstrated for long-range XYZ spin chains. revision: partial

  2. Referee: [Abstract] The abstract asserts numerical demonstrations of system-size independence and distinguishing power of long-time averages and fluctuations, yet provides no information on the range of system sizes examined, the presence or absence of error bars, the precise definition of the long-time window, or the numerical procedure for the Haar average. These omissions prevent verification that the reported behavior is not an artifact of post-hoc choices or finite-size effects.

    Authors: The main text and methods section already specify the system sizes (N = 4–12), the long-time averaging window after saturation, statistical error bars obtained from multiple disorder realizations, and the explicit Haar-averaging protocol over random unitaries. Because the abstract is length-limited we will add a concise clause indicating the range of system sizes examined and will ensure the methods section contains all numerical parameters for full reproducibility. revision: yes

Circularity Check

0 steps flagged

No circularity: aSTC defined from standard mutual information and benchmarked externally against OTOC

full rationale

The paper defines the Haar-averaged sum of total correlations (aSTC) directly from quantum mutual information on dynamically generated states, without any parameter fitting or self-referential construction. It then numerically compares long-time averages and fluctuations of aSTC to the independent, externally established OTOC benchmark in the long-range XYZ model. No step reduces a claimed prediction to a fitted input by construction, no uniqueness theorem is imported via self-citation, and the model choice is presented as an illustrative family rather than a definitional input. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities can be extracted. The work relies on standard definitions of quantum mutual information, Haar averaging, and Markovian/non-Markovian master equations whose details are not provided.

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