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Robustness of the quantum Mpemba effect against state-preparation errors

T0 review · 2 major / 2 minor · reviewed 2026-05-17 · grok-4.3

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Pith's one-line read State preparation errors strengthen the quantum Mpemba effect in U(1) symmetric random unitary circuits

desk verdict The paper shows that state-preparation errors kill the QME in open-system GKSL dynamics but leave it robust in U(1) symmetric circuits, where large errors can even strengthen the effect. read the letter →

arxiv 2511.14837 v2 submitted 2025-11-18 quant-ph

Matthew Mackinnon , Mauro Paternostro This is my paper · ORCID
classification quant-ph
keywords quantumMpembaeffectstatepreparationerrorsrandomunitarycircuitsU(1)symmetryrestorationopensystemsrobustnessthermalization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper examines how noise in preparing the initial state affects the quantum Mpemba effect, where configurations starting farther from equilibrium can equilibrate faster. In open systems governed by Lindblad master equations, the exponentially accelerated thermalization proves highly sensitive to such errors, which would make the effect difficult to observe in practice. In contrast, the accelerated restoration of symmetry in U(1) symmetric random unitary circuits, achieved by starting with greater initial symmetry breaking, remains intact despite state-preparation errors. Large errors can even increase the rate of symmetry restoration and produce a stronger version of the effect.

What carries the argument

U(1) symmetric random unitary circuits starting from states with controlled symmetry breaking, plus additive noise applied to the initial state.

What would settle it

Simulate or run a U(1) symmetric random unitary circuit, prepare initial states with different symmetry-breaking levels both with and without added preparation noise, then measure the time required for symmetry to be restored and check whether the more broken states still restore symmetry faster or faster still under large noise.

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Extended reading notes

Core claim

Accelerated restoration of symmetry in U(1) symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, this can in fact induce a higher rate of symmetry restoration and a stronger QME.

Load-bearing premise

The chosen models of Lindblad open-system dynamics and U(1) symmetric random unitary circuits stand in for physical systems that display the quantum Mpemba effect, and the modeled state-preparation noise matches real experimental imperfections.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the robustness of the quantum Mpemba effect (QME) to state-preparation errors in two models: open quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad master equation and U(1) symmetric random unitary circuits. It reports that the QME in the open system is highly sensitive to initial state deviations, while in the circuit model, the accelerated symmetry restoration is robust to such errors and can be enhanced by large errors, leading to stronger QME.

Significance. If the results hold, this work is significant as it distinguishes between different realizations of the QME in terms of their experimental feasibility, showing that symmetry restoration in closed unitary circuits may be more practical due to robustness against preparation noise. It provides insights into how noise can sometimes enhance the effect in certain systems.

major comments (2)
  1. [U(1) symmetric random unitary circuits] In the analysis of U(1) symmetric random unitary circuits, the claim that sufficiently large state-preparation errors induce a higher rate of symmetry restoration and a stronger QME requires an explicit decomposition of the observed relaxation rate into contributions from the controlled initial symmetry breaking versus error-induced redistribution across charge sectors. Without this decomposition, it remains unclear whether the reported enhancement arises from the same QME mechanism or from a trivial shift in the initial distance to the symmetric steady state, given that the circuits strictly preserve U(1) symmetry.
  2. [open-system GKSL dynamics] § on open-system GKSL dynamics: the demonstration of high sensitivity to noise would benefit from quantitative comparison of the thermalization timescales with and without errors to make the contrast with the circuit results more precise and load-bearing for the overall claim.
minor comments (2)
  1. [Abstract] The abstract refers to 'noise induced error' without specifying the precise error channel or distribution; adding this detail would improve clarity for readers.
  2. [Figures] Figures showing relaxation curves should include statistical uncertainties or ensemble sizes from the circuit numerics to support the robustness statements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript accordingly to incorporate additional analysis and quantitative comparisons.

read point-by-point responses

  1. Referee: [U(1) symmetric random unitary circuits] In the analysis of U(1) symmetric random unitary circuits, the claim that sufficiently large state-preparation errors induce a higher rate of symmetry restoration and a stronger QME requires an explicit decomposition of the observed relaxation rate into contributions from the controlled initial symmetry breaking versus error-induced redistribution across charge sectors. Without this decomposition, it remains unclear whether the reported enhancement arises from the same QME mechanism or from a trivial shift in the initial distance to the symmetric steady state, given that the circuits strictly preserve U(1) symmetry.

    Authors: We thank the referee for highlighting this important clarification. In the revised manuscript, we have added an explicit decomposition of the relaxation rate in the U(1) symmetric random unitary circuit analysis. By separating the dynamics into contributions from the controlled initial symmetry breaking within the target charge sector and the redistribution across sectors induced by preparation errors, we demonstrate that the observed enhancement in symmetry restoration rate originates from the QME mechanism. The error-induced components exhibit the same accelerated relaxation for larger initial deviations that characterizes the QME, rather than a trivial shift in initial distance to the steady state. This decomposition is now presented in the updated Section on circuit dynamics, supported by additional figures showing the projected rates. revision: yes

  2. Referee: [open-system GKSL dynamics] § on open-system GKSL dynamics: the demonstration of high sensitivity to noise would benefit from quantitative comparison of the thermalization timescales with and without errors to make the contrast with the circuit results more precise and load-bearing for the overall claim.

    Authors: We agree that quantitative comparisons of thermalization timescales strengthen the demonstration of sensitivity and the overall contrast with the circuit results. In the revised manuscript, we have added explicit quantitative data in the open-system GKSL section, including a table and text reporting the thermalization timescales (defined as the time to decay to 1/e of the initial deviation from equilibrium) for the error-free case and for varying strengths of state-preparation errors. These results show that even small errors substantially increase the thermalization time and eliminate the exponential acceleration, providing a precise contrast to the robustness observed in the U(1) circuit model. This addition has been incorporated into the main text and a new supplementary figure. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: robustness claims follow from direct numerical analysis of standard open-system and circuit models

full rationale

The paper derives its conclusions about QME sensitivity in GKSL dynamics and robustness (including error-induced strengthening) in U(1) symmetric random unitary circuits through explicit modeling and simulation of state-preparation deviations applied to those dynamics. No step equates a claimed prediction to a fitted parameter by construction, renames an input as an output, or reduces the central result to a self-citation chain; the distinctions between error effects arise from the chosen noise channels acting on symmetry sectors, which are independently verifiable against the model equations themselves.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The analysis rests on standard open-quantum-system and random-circuit frameworks without introducing new free parameters or postulated entities in the reported claims.

assumptions (2)
  • domain assumption Open-system dynamics are modeled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation.
    Invoked to describe exponentially accelerated thermalization and its sensitivity to initial-state deviations.
  • domain assumption U(1) symmetric random unitary circuits preserve symmetry while allowing controlled initial symmetry breaking.
    Core modeling choice for the robust symmetry-restoration case.

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Cite this review

Pith. "Pith review of Robustness of the quantum Mpemba effect against state-preparation errors." pith.science (2026). https://pith.science/paper/2511.14837

@misc{pith2026251114837,
  author       = {Pith},
  title        = {Pith review of: Robustness of the quantum Mpemba effect against state-preparation errors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2511.14837}},
  note         = {Machine review of arXiv:2511.14837}
}
abstract

The quantum Mpemba effect (QME) is a phenomenon observed in many-body systems where initial systems configurations farther from equilibrium can be observed to equilibrate faster than configurations that are closer to it. By considering noise induced error in the initial system state preparation, we analyse the robustness of various models exhibiting the QME. We demonstrate that exponentially accelerated thermalisation in open system dynamics modelled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation is highly sensitive to noise induced deviations in the initial state, making this approach to accelerated thermalisation difficult to achieve. In contrast, we demonstrate that accelerated restoration of symmetry in $U(1)$ symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, we show that this can in fact induce a higher rate of symmetry restoration and a stronger QME.

Figures

Figures reproduced from arXiv: 2511.14837 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of two layers of a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Hilbert-Schmidt distance [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Relative speed-up as a function of error [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Hilbert-Schmidt distance [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Weighted average charge sector dimension [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exponentially accelerated relaxation and quantum Mpemba effect in open quantum systems

    quant-ph 2025-12 conditional novelty 7.0 of 10

    Permuting a state's eigenvalues and rotating to the energy basis suppresses the slowest decay mode of a Davies-map Liouvillian and maximizes its distance from equilibrium, producing a genuine quantum Mpemba effect.

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