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arxiv: 2605.16029 · v1 · pith:WESTINK5new · submitted 2026-05-15 · 🪐 quant-ph · cond-mat.dis-nn· cond-mat.quant-gas· cond-mat.stat-mech· cond-mat.str-el

Born-rule statistical dynamical quantum phase transitions under measurement

Guan-Hua Chen , Guo-Yi Zhu This is my paper

Pith reviewed 2026-05-20 19:02 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nncond-mat.quant-gascond-mat.stat-mechcond-mat.str-el
keywords Born ruledynamical quantum phase transitionsquantum measurementsIsing chainquantum quenchmixed statesYang-Lee-Fisher zerosmeasurement-based quantum computation
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The pith

Statistical sampling of Born-rule measurement outcomes recovers dynamical quantum phase transitions in quenched Ising chains.

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

The paper examines dynamical quantum phase transitions, defined as nonanalytic changes in the return probability after a quantum quench, but incorporates the randomness of quantum measurements. Instead of a single evolved state, it studies the full ensemble of possible post-measurement states distributed according to the Born rule in a one-dimensional Ising chain. This ensemble is treated as equivalent to a mixed state arising from maximal dephasing noise, which is then mapped to a statistical model possessing an effective energy spectrum. An average dynamical free energy is introduced to characterize the ensemble, and the authors demonstrate that the nonanalytic features of the original transitions reappear under high-moment averages while the effective levels delocalize after critical times. Analytic continuation to complex times further shows the vanishing of Yang-Lee-Fisher zeros together with emergent level crossings.

Core claim

Dynamical quantum phase transitions occur at times when a quantum state exhibits a nonanalytic change in its return probability, viewed as the probability of collapsing the evolved state to the initial state by quantum measurement. We perform statistical characterization for all the possible post-measurement states distributed according to the Born's rule by sampling a one-dimensional quantum Ising chain after a quantum quench dynamics. The statistical ensemble can also be viewed as a mixed state when the time evolved state is subjected to maximally dephasing noise in a certain basis. We map the distribution to a statistical model and characterize its effective energy spectrum, and introduce

What carries the argument

The average dynamical free energy constructed from the effective energy spectrum of the statistical model that represents the Born-rule ensemble of post-measurement states under maximal dephasing.

If this is right

  • Nonanalytic signatures of DQPTs reappear when the return probability is averaged over higher statistical moments of the Born-rule outcomes.
  • The effective energy levels in the mapped statistical model spread out after the critical times.
  • Yang-Lee-Fisher zeros vanish and level crossings appear when time is continued into the complex plane near the critical points.
  • A protocol of single-qubit measurements on a two-dimensional cluster state can simulate the underlying unitary evolution for experimental study of these transitions.

Where Pith is reading between the lines

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

  • The same statistical mapping could be tested with other forms of decoherence to see how mixed-state dynamics alter nonequilibrium transitions.
  • The proposed cluster-state protocol indicates that existing quantum hardware could directly implement the required sampling without maintaining full coherence.
  • Insights from the delocalized level distribution may inform structured sampling techniques in quantum circuits where measurement randomness plays a central role.

Load-bearing premise

The statistical ensemble of Born-rule sampled post-measurement states can be equivalently viewed as a mixed state produced by maximally dephasing noise in a certain basis, enabling the mapping to a statistical model with an effective energy spectrum.

What would settle it

Numerical sampling of post-measurement states in the quenched one-dimensional Ising chain to check whether high-moment averages of the return probability display nonanalyticities exactly at the predicted critical times and whether the effective energy levels become delocalized immediately afterward.

Figures

Figures reproduced from arXiv: 2605.16029 by Guan-Hua Chen, Guo-Yi Zhu.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_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_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
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Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
read the original abstract

Dynamical quantum phase transitions (DQPTs) occur at times when a quantum state exhibits a nonanalytic change in its return probability. This can be viewed as the probability of collapsing the evolved state to the initial state by quantum measurement. However, the initial wave function usually has exponentially small amplitude in the late time evolved state. Here we perform statistical characterization for all the possible post-measurement states distributed according to the Born's rule, by sampling a one-dimensional quantum Ising chain after a quantum quench dynamics. The statistical ensemble can also be viewed as a mixed state when the time evolved state is subjected to maximally dephasing noise in a certain basis. We map the distribution to a statistical model and characterize its effective "energy" spectrum, and introduce the average dynamical free energy, establishing a framework for the statistical DQPTs. We show the recovering of DQPT under high-moment average and a delocalized level distribution following critical times. Through analytic continuation into the complex time plane, we demonstrate the vanishing of Yang-Lee-Fisher zeros and the emergent level crossing near critical times. Finally, we propose a measurement-based quantum computation protocol to simulate the unitary evolution via single-qubit measurements on a two-dimensional cluster state. Our results provide a way for experimentally investigating statistical DQPTs in quantum devices, shedding light on the structured circuit sampling with insights from DQPT and generalizing the understanding of mixed state due to decoherence beyond equilibrium.

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 manuscript investigates statistical aspects of dynamical quantum phase transitions (DQPTs) by sampling post-measurement states according to Born's rule in a one-dimensional quantum Ising chain after a quench. It maps the ensemble to a mixed state under maximal dephasing, defines an average dynamical free energy from an effective statistical model, demonstrates recovery of DQPT non-analyticities via high-moment averages, shows delocalized level distributions and vanishing Yang-Lee-Fisher zeros through analytic continuation in complex time, and proposes a measurement-based quantum computation protocol for simulation.

Significance. If the central mapping and recovery hold, the work offers a novel statistical framework for DQPTs that could facilitate experimental studies in quantum devices under decoherence. It provides insights into mixed-state dynamics and structured circuit sampling. The analytic continuation results and the proposed protocol are potentially significant extensions, though their robustness depends on verifying the higher-moment equivalence.

major comments (2)
  1. [§4] §4 (Mapping to statistical model and definition of average dynamical free energy): The equivalence between the Born-rule sampled pure states and the maximally dephased mixed state ρ = ∑ p_n |n⟩⟨n| reproduces the first moment correctly, but the manuscript does not provide explicit verification that higher moments of the return probabilities are preserved when constructing the effective energy spectrum. This is load-bearing for the central claim that high-moment averages recover the original DQPT non-analyticities.
  2. [§5] §5 (Analytic continuation into complex time plane): The demonstration of vanishing Yang-Lee-Fisher zeros and emergent level crossings near critical times is based on the effective spectrum derived from the statistical model. Without direct numerical comparison to independent Born-rule sampling (e.g., via Monte Carlo benchmarks of the return amplitude distribution), the extrapolation risks circularity as noted in the definition of the average dynamical free energy from the sampled distribution itself.
minor comments (2)
  1. [Abstract] Abstract: The phrasing 'recovering of DQPT' is grammatically awkward and should be revised to 'recovery of DQPTs' for clarity.
  2. [Figures] Figure captions (e.g., level distribution plots): Include sampling size, error bars, or convergence checks to support the delocalized distribution claim following critical times.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below and indicate revisions to the manuscript where the concerns are valid.

read point-by-point responses

  1. Referee: [§4] §4 (Mapping to statistical model and definition of average dynamical free energy): The equivalence between the Born-rule sampled pure states and the maximally dephased mixed state ρ = ∑ p_n |n⟩⟨n| reproduces the first moment correctly, but the manuscript does not provide explicit verification that higher moments of the return probabilities are preserved when constructing the effective energy spectrum. This is load-bearing for the central claim that high-moment averages recover the original DQPT non-analyticities.

    Authors: We agree that explicit verification of higher-moment preservation is necessary to support the central claim. The original manuscript establishes the first-moment equivalence via the dephased mixed state and shows recovery of DQPT features in high-moment averages of the effective statistical model, but does not include direct numerical checks comparing higher moments from independent Born-rule sampling against the effective spectrum. We will add such verification in the revised manuscript, including Monte Carlo sampling of post-measurement states and explicit comparison of moment distributions up to orders where non-analyticities appear. revision: yes

  2. Referee: [§5] §5 (Analytic continuation into complex time plane): The demonstration of vanishing Yang-Lee-Fisher zeros and emergent level crossings near critical times is based on the effective spectrum derived from the statistical model. Without direct numerical comparison to independent Born-rule sampling (e.g., via Monte Carlo benchmarks of the return amplitude distribution), the extrapolation risks circularity as noted in the definition of the average dynamical free energy from the sampled distribution itself.

    Authors: We acknowledge the risk of circularity in relying solely on the effective spectrum for the analytic continuation results. The effective model is constructed from the ensemble averages, so independent validation against raw Born-rule samples is warranted. In the revision we will include direct Monte Carlo benchmarks of the return amplitude distribution from sampled post-measurement states and compare the resulting zero locations and level-crossing features to those obtained via analytic continuation of the effective free energy, confirming that the qualitative behavior is preserved. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper starts from the Born-rule post-measurement ensemble after a quench, notes its equivalence to a maximally dephased mixed state ρ = ∑ p_n |n⟩⟨n|, maps the resulting distribution to a statistical model with an effective energy spectrum, and defines the average dynamical free energy within that model. It then reports recovery of DQPT non-analyticities under high-moment averages, vanishing Yang-Lee-Fisher zeros under analytic continuation, and emergent level crossings. None of these steps reduce by the paper's own equations to a redefinition of the input distribution or to a fitted parameter renamed as a prediction; the mapping supplies independent structure for the subsequent statistical characterization, and the reported results are presented as consequences rather than identities. No self-citations appear in the provided text as load-bearing premises.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework rests on standard quantum postulates and the specific choice of the Ising chain; no obvious fitted parameters or new particles are introduced in the abstract, but the effective statistical model and average free energy are constructed quantities.

axioms (2)
  • standard math Born's rule governs the probabilities of post-measurement states
    Directly invoked to generate the statistical ensemble from the time-evolved state
  • domain assumption The one-dimensional quantum Ising chain under sudden quench dynamics
    Chosen as the concrete system for performing the sampling and analysis
invented entities (1)
  • average dynamical free energy no independent evidence
    purpose: To characterize the effective energy spectrum of the statistical ensemble
    New quantity introduced to establish the statistical DQPT framework

pith-pipeline@v0.9.0 · 5802 in / 1408 out tokens · 70510 ms · 2026-05-20T19:02:19.381330+00:00 · methodology

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