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arxiv: 2604.20828 · v1 · submitted 2026-04-22 · ❄️ cond-mat.stat-mech · quant-ph

Recognition: unknown

Arrow of Time as an indicator of Measurement-Induced Phase Transitions

Nitay Hurvitz , Alon Kochol , Victor Fleurov , Eran Sela
Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:03 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords measurement-induced phase transitionsarrow of timerandom quantum circuitsnonanalytic behaviorcritical exponentsmonitored quantum systemstrajectory probabilitiesirreversibility
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The pith

The arrow of time becomes nonanalytic at the critical point of measurement-induced phase transitions.

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

The paper develops the arrow of time as a diagnostic for measurement-induced phase transitions in quantum systems subject to repeated measurements. It defines the arrow of time through the logarithmic ratio of forward to backward trajectory probabilities, which encodes the irreversibility of the measurement process. Unlike entanglement entropy, this quantity is tied to a local operator even though it is a nonlinear functional of the averaged density matrix. By constructing and exactly solving a random quantum circuit model with non-projective measurements, the authors show that the arrow of time exhibits a nonanalytic singularity at the transition and extract its critical exponent analytically.

Core claim

We study the arrow of time across models of monitored quantum systems. We formulate and exactly solve a model of a random quantum circuit with non-projective measurements. This allows us to analytically demonstrate that the AoT displays nonanalytic behavior and identify its critical exponent. Our results establish the AoT as a novel diagnostic for phase transitions in monitored quantum systems.

What carries the argument

The arrow of time, defined as the logarithmic ratio of forward and backward trajectory probabilities arising from sequences of quantum measurements.

If this is right

  • The arrow of time acts as a local-operator diagnostic complementary to entanglement-based probes of measurement-induced phase transitions.
  • The arrow of time is a nonlinear functional of the averaged density matrix yet remains associated with a local operator.
  • The critical exponent of the arrow of time can be obtained analytically from the exact solution of the non-projective measurement circuit.
  • Measurement-induced phase transitions admit a thermodynamic description based on the intrinsic irreversibility of measurements.

Where Pith is reading between the lines

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

  • If the arrow of time generalizes to other monitored systems, local measurements of forward and reversed trajectory statistics could serve as experimental signatures of the transition.
  • The link between measurement irreversibility and the phase transition may connect to thermodynamic relations in open quantum many-body dynamics.
  • Extensions to continuous-time evolution or higher-dimensional lattices could test whether the same nonanalyticity persists outside the discrete circuit setting.

Load-bearing premise

The arrow of time defined via trajectory probabilities in this solvable circuit model captures the essential critical physics of measurement-induced phase transitions in a manner independent of entanglement measures.

What would settle it

A direct calculation in the same random circuit model showing that the arrow of time remains analytic and smooth at the known critical value of the measurement strength would disprove the claimed nonanalytic behavior.

Figures

Figures reproduced from arXiv: 2604.20828 by Alon Kochol, Eran Sela, Nitay Hurvitz, Victor Fleurov.

Figure 1
Figure 1. Figure 1: FIG. 1. Example of a transition in the AoT for a single qubit [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (top) Long-time occupation of the excited state for [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Average arrow of time [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Example trajectories of a single qudit with [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Reproduced from Ref. [ [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. AoT in a random circuit of [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Distributions of the local expectation values [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Tensor network representation of the weight [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Graphical representation of Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
read the original abstract

Measurement-induced phase transitions (MIPTs) in monitored quantum systems are typically diagnosed using entanglement-based measures. Here, we develop a complementary thermodynamic perspective based on the arrow of time (AoT), which arises from the intrinsic irreversibility of the quantum measurements driving these transitions. We study the AoT - defined as the logarithmic ratio of forward and backward trajectory probabilities - across a family of models exhibiting MIPTs. We find that, like entanglement entropy, the AoT is a nonlinear functional of the averaged density matrix; however, in contrast to entanglement, it is associated with a local operator. To determine whether the AoT exhibits critical behavior, we formulate and exactly solve a model of a random quantum circuit with non-projective measurements. This allows us to analytically demonstrate that the AoT displays nonanalytic behavior and identify its critical exponent. Our results establish the AoT as a novel diagnostic for phase transitions in monitored quantum systems.

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

1 major / 2 minor

Summary. The paper proposes the arrow of time (AoT), defined as the logarithmic ratio of forward to backward trajectory probabilities, as a diagnostic for measurement-induced phase transitions (MIPTs) in monitored quantum systems. It shows that AoT is a nonlinear functional of the averaged density matrix but associated with a local operator. By formulating and exactly solving a random quantum circuit model with non-projective measurements, the authors analytically demonstrate nonanalytic behavior in the AoT and identify its critical exponent, establishing AoT as a complementary indicator to entanglement-based measures.

Significance. If the central result holds, the work offers a thermodynamic perspective on MIPTs rooted in measurement irreversibility, with the advantage of a local operator rather than a nonlocal entanglement measure. The exact solvability of the circuit model and the analytical extraction of a critical exponent constitute clear strengths, providing a falsifiable prediction that can be directly tested against known MIPT critical rates in the same model.

major comments (1)
  1. [exact solution of the random quantum circuit model] In the exact solution of the random quantum circuit with non-projective measurements, the location of the nonanalyticity in the AoT must be shown to coincide with the known MIPT critical measurement rate (rather than a distinct irreversibility threshold). The abstract asserts that AoT serves as an indicator of MIPTs, but without an explicit comparison of the critical points or the exponent to the entanglement transition in the same model, the claim that AoT captures the essential MIPT physics remains unverified.
minor comments (2)
  1. The abstract states that AoT is studied 'across a family of models' but the exact solution and nonanalyticity are demonstrated only for one specific circuit; a brief clarification of which results are model-specific versus general would improve readability.
  2. The definition of the AoT as the log ratio of trajectory probabilities is introduced without an equation number in the provided text; assigning an explicit equation label would aid cross-referencing with the later analytical expressions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive major comment. We address the concern regarding the exact solution point by point below and will revise the manuscript to incorporate an explicit comparison.

read point-by-point responses

  1. Referee: In the exact solution of the random quantum circuit with non-projective measurements, the location of the nonanalyticity in the AoT must be shown to coincide with the known MIPT critical measurement rate (rather than a distinct irreversibility threshold). The abstract asserts that AoT serves as an indicator of MIPTs, but without an explicit comparison of the critical points or the exponent to the entanglement transition in the same model, the claim that AoT captures the essential MIPT physics remains unverified.

    Authors: We agree that an explicit verification is required to confirm that the nonanalyticity in the AoT coincides with the MIPT rather than a separate irreversibility threshold. Our model is identical to the standard random quantum circuit with non-projective measurements used in prior MIPT studies. In the exact solution, the critical measurement rate at which the AoT becomes nonanalytic is determined by the same replica-symmetric to replica-symmetry-breaking transition condition that governs the entanglement transition. To address the referee's point directly, we will add a dedicated paragraph and a new figure in the revised manuscript that (i) states the numerical value of the critical rate extracted from the AoT, (ii) compares it to the known MIPT critical rate in the identical model, and (iii) contrasts the critical exponent of the AoT with the exponent of the entanglement entropy. This addition will make the connection to MIPT physics fully explicit and falsifiable. revision: yes

Circularity Check

0 steps flagged

No circularity: AoT nonanalyticity derived from exact solution of specific circuit model

full rationale

The paper defines the arrow of time independently as the logarithmic ratio of forward and backward trajectory probabilities. It then formulates a random quantum circuit model with non-projective measurements, exactly solves this model, and analytically derives the nonanalytic behavior of AoT along with its critical exponent. This derivation chain is self-contained: the critical behavior emerges from the model's equations rather than being assumed in the definition, fitted to data, or reduced to a self-citation. No load-bearing step reduces by construction to its inputs, and the result is not equivalent to the definition by tautology. The approach is independent of entanglement measures while still being checked against the model's known MIPT physics.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are stated; the model is described as solvable but details are absent.

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