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arxiv: 2509.14329 · v3 · submitted 2025-09-17 · 🪐 quant-ph · cond-mat.dis-nn· cond-mat.mes-hall· cond-mat.stat-mech· hep-th

Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics

Surajit Bera , Igor V. Gornyi , Sumilan Banerjee , Yuval Gefen This is my paper

Pith reviewed 2026-05-18 15:35 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nncond-mat.mes-hallcond-mat.stat-mechhep-th
keywords measurement-only dynamicsvolume-law entanglementgeneralized measurementsfermionic chainnon-unitary dynamicsquantum trajectoriesentanglement generationancilla qubits
0
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The pith

Non-commuting local measurements generate volume-law entanglement in fermionic chains without unitary dynamics

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

The paper establishes that repeated generalized measurements performed by locally coupling a main fermionic chain to detector qubits can produce long-time states with volume-law entanglement and mutual information purely through non-unitary dynamics. This matters because local measurements are conventionally expected to degrade entanglement, yet here non-commuting measurements build extensive correlations across the chain. The construction shows this occurs even when restricted to one-body operators, while measurements of non-local higher-body operators can suppress the effect by adding kinetic constraints. The work also tracks entanglement statistics along individual trajectories and their convergence to stationary distributions under limited ergodicity.

Core claim

In a one-dimensional model with a main fermionic chain and auxiliary detector qubits, long-time states with volume-law entanglement or mutual information are generated between different parts of the main chain purely through non-unitary measurement dynamics, and such large-entanglement generation can be achieved using only the measurements of one-body operators.

What carries the argument

Generalized measurements via local coupling to detector qubits that implement non-commuting projections on the fermionic chain, driving entanglement growth in the absence of unitary evolution.

If this is right

  • Volume-law entanglement arises from one-body operator measurements alone in a measurement-only setting.
  • Higher-body operator measurements introduce kinetic constraints that reduce entanglement generation.
  • Entanglement measures along quantum trajectories approach stationary distributions with limited ergodicity.
  • Non-random measurement protocols allow controlled entanglement generation in non-unitary many-body dynamics.

Where Pith is reading between the lines

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

  • The protocol suggests a route to entanglement generation in quantum hardware that relies primarily on local measurement controls.
  • It links to measurement-induced phase transitions but reverses their typical role from entanglement suppression to creation.
  • Similar measurement-only constructions could be explored in two-dimensional lattices or with feedback rules based on outcomes.
  • Direct tests involve tracking subsystem entanglement entropy scaling in exact or approximate simulations of the dynamics.

Load-bearing premise

That non-commuting generalized measurements on local one-body operators, implemented by coupling to ancilla qubits with no unitary component, suffice to produce volume-law entangled states.

What would settle it

Numerical evolution of the measurement protocol on a finite chain where the long-time entanglement entropy of a subsystem scales linearly with boundary length instead of subsystem volume.

Figures

Figures reproduced from arXiv: 2509.14329 by Igor V. Gornyi, Sumilan Banerjee, Surajit Bera, Yuval Gefen.

Figure 1
Figure 1. Figure 1: FIG. 1. The system-detector setup for measurement only dy [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The probability density function [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The trajectory-averaged entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The probability density [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) The stationary probability density of [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Stationary probability density function [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: ) corresponds to quantum trajectories with the maximum Born weight. These trajectories consist en￾tirely of no-click (↑) outcomes for the detectors. Accord￾ing to Eq. (5a), even all no-click events can lead to a non￾trivial evolution of a superposition state, such as |Ψrs⟩, where no-click (↑) outcomes reduce the relative weight of states with pair(s) of occupied or empty neighboring sites by factor(s) of … view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Probability distribution [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. System-size scaling of long-time entanglement entropies and the mutual information for product initial state [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. System-size scaling of long-time entanglement entropies and the mutual information for random superposition initial [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. System-size scaling of average stationary-state entanglement entropies and the mutual information for random super [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. System-size scaling of average stationary state entanglement entropies and mutual information for product initial [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17 [PITH_FULL_IMAGE:figures/full_fig_p022_17.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. (a) The stationary probability density of [PITH_FULL_IMAGE:figures/full_fig_p023_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Stationary probability density function [PITH_FULL_IMAGE:figures/full_fig_p024_20.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. The time ( [PITH_FULL_IMAGE:figures/full_fig_p024_22.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Probability distribution [PITH_FULL_IMAGE:figures/full_fig_p025_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. (a) Stationary probability distribution [PITH_FULL_IMAGE:figures/full_fig_p026_25.png] view at source ↗
Figure 27
Figure 27. Figure 27: FIG. 27. The inverse participation ratio (IPR) for the station [PITH_FULL_IMAGE:figures/full_fig_p026_27.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26. The inverse participation ratio (IPR) for the sta [PITH_FULL_IMAGE:figures/full_fig_p026_26.png] view at source ↗
Figure 28
Figure 28. Figure 28: FIG. 28. The system-size scaling of long-time entanglement entropies and mutual information for the equal superposition [PITH_FULL_IMAGE:figures/full_fig_p028_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: FIG. 29. The system-size scaling of stationary-state entanglement entropies and mutual information for the equal superposition [PITH_FULL_IMAGE:figures/full_fig_p028_29.png] view at source ↗
read the original abstract

Repeated local measurements typically have adversarial effects on entangling unitary dynamics, as local measurements usually degrade entanglement. However, recent works on measurement-only dynamics have shown that strongly entangled states can be generated solely through non-commuting random multi-site and multi-spin projective measurements. In this work, we explore a generalized measurement setup in a system without intrinsic unitary dynamics and show that volume-law entangled states can be generated through local, non-random, yet non-commuting measurements. Specifically, we construct a one-dimensional model comprising a main fermionic chain and an auxiliary (ancilla) chain, where generalized measurements are performed by locally coupling the system to detector qubits. Our results demonstrate that long-time states with volume-law entanglement or mutual information are generated between different parts of the main chain purely through non-unitary measurement dynamics. Remarkably, we find that such large-entanglement generation can be achieved using only the measurements of one-body operators. Moreover, we show that measurements of non-local higher-body operators can be used to control and reduce entanglement generation by introducing kinetic constraints to the dynamics. We discuss the statistics of entanglement measures along the quantum trajectories, the approach to stationary distributions of entanglement or long-time steady states, and the associated notions of limited ergodicity in the measurement-only dynamics. Our findings highlight the potential of non-random measurement protocols for controlled entanglement generation and the study of non-unitary many-body 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 manuscript constructs a one-dimensional fermionic chain coupled locally to an auxiliary ancilla chain of detector qubits. Generalized measurements of one-body operators are applied repeatedly in the absence of intrinsic unitary dynamics. The central claim is that this protocol generates long-time states on the main chain that exhibit volume-law scaling of bipartite entanglement entropy and mutual information, and that measurements of non-local higher-body operators can be used to impose kinetic constraints that reduce the generated entanglement. The work further examines trajectory statistics, approach to stationary distributions, and limited ergodicity under the measurement-only dynamics.

Significance. If the claims are substantiated, the result is significant: it demonstrates that volume-law entanglement can be produced by purely non-unitary dynamics using only local, non-random, one-body measurements, contrary to the usual expectation that local measurements drive area-law or logarithmic scaling. The ancilla-mediated generalized measurement protocol and the control via higher-body operators provide a concrete, falsifiable construction that could be relevant to studies of measurement-induced phases and controlled entanglement generation.

major comments (2)
  1. [§2] §2 (model construction): local one-body operators on disjoint sites commute, so the non-commutativity required for volume-law generation must arise either from the sequential choice of measurement bases or from the ancilla-coupling protocol itself. The manuscript must explicitly demonstrate that the effective back-action after tracing out the ancilla remains strictly local and does not introduce implicit non-local correlations that could mimic unitary evolution.
  2. [Numerical results] Numerical evidence for volume-law scaling (results section): the abstract and main text assert linear scaling of entanglement or mutual information, yet no details are provided on the number of trajectories sampled, error bars, finite-size scaling collapse, or post-selection criteria for long-time states. Without these, it is impossible to rule out that the reported volume law is an artifact of trajectory selection or insufficient sampling.
minor comments (2)
  1. Notation for the generalized measurement operators and the ancilla coupling strength should be defined more explicitly in the main text rather than deferred to appendices.
  2. Figure captions for entanglement scaling plots should include the subsystem sizes used and the fitting ranges for the linear regime.

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 help clarify key aspects of the work. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [§2] §2 (model construction): local one-body operators on disjoint sites commute, so the non-commutativity required for volume-law generation must arise either from the sequential choice of measurement bases or from the ancilla-coupling protocol itself. The manuscript must explicitly demonstrate that the effective back-action after tracing out the ancilla remains strictly local and does not introduce implicit non-local correlations that could mimic unitary evolution.

    Authors: We agree that an explicit demonstration of the locality of the effective back-action is necessary for rigor. The non-commutativity arises from the sequential application of measurements in different bases via the ancilla protocol. In the revised manuscript we will expand §2 with a detailed derivation of the effective Kraus operators obtained after tracing out the ancilla qubits. This derivation will confirm that the back-action remains strictly local (acting only on the sites directly coupled to the ancilla) and does not generate implicit non-local correlations that could be mistaken for unitary evolution. We will also add a short paragraph clarifying how the ancilla-mediated generalized measurements produce the required non-commuting operations without violating locality. revision: yes

  2. Referee: [Numerical results] Numerical evidence for volume-law scaling (results section): the abstract and main text assert linear scaling of entanglement or mutual information, yet no details are provided on the number of trajectories sampled, error bars, finite-size scaling collapse, or post-selection criteria for long-time states. Without these, it is impossible to rule out that the reported volume law is an artifact of trajectory selection or insufficient sampling.

    Authors: We acknowledge that the numerical section lacks sufficient methodological detail. In the revised manuscript we will add a dedicated paragraph (or subsection) in the results section that specifies: (i) the number of trajectories sampled for each data point (typically 1000–2000 for the system sizes shown), (ii) the statistical error bars obtained from trajectory averaging, (iii) finite-size scaling collapse performed across multiple chain lengths, and (iv) the post-selection criteria used to identify long-time states (e.g., averaging after a fixed number of measurement steps once entanglement has saturated). These additions will allow readers to assess the robustness of the volume-law scaling and rule out sampling artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit model construction and trajectory simulation generate the reported volume-law states

full rationale

The paper presents a concrete Hamiltonian-free protocol with ancilla-coupled generalized measurements on a fermionic chain and reports the resulting entanglement scaling from direct evolution of quantum trajectories. No parameter is fitted to the target volume-law scaling and then re-used as a prediction; the central result follows from the defined measurement operators and the stochastic update rules rather than from any self-referential definition or prior self-citation that would close the loop. The non-commutativity is introduced explicitly by the choice of sequential local one-body operators and the ancilla coupling, which is an input to the construction rather than an output derived from the entanglement measure itself. Consequently the derivation chain remains open and externally verifiable by independent simulation of the same protocol.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum measurement postulates and the assumption that the chosen local coupling to ancilla qubits produces non-commuting measurement operators; no explicit free parameters or new entities are named in the abstract.

axioms (1)
  • domain assumption Projective measurements on non-commuting operators drive the system into a steady distribution of entanglement values
    Invoked when the abstract states that long-time states with volume-law entanglement are generated purely through non-unitary measurement dynamics.

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Reference graph

Works this paper leans on

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