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arxiv: 2604.22022 · v1 · submitted 2026-04-23 · 🪐 quant-ph · cond-mat.stat-mech

Entanglement and information scrambling in long-range measurement-only circuits

Abigail McClain Gomez , Fiona Abney-McPeek , Hong-Ye Hu , Susanne F. Yelin , Ceren B. Da\u{g} This is my paper

Pith reviewed 2026-05-09 21:18 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords measurement-only circuitslong-range measurementsentanglement transitionsinformation scramblingClifford circuitsvolume-law entanglementancilla purificationstatistical mechanics mapping
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The pith

Structured long-range measurement circuits sustain volume-law entanglement with rapid ancilla purification and no scrambling.

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

The paper studies one-dimensional measurement-only Clifford circuits that apply long-range parity checks, varying both the interaction range and the number of measurements per layer. It compares random-basis protocols, where each measurement picks XX, YY or ZZ at random, to single-basis protocols that fix the measurement type within each layer but change it across layers. In the structured single-basis case the authors identify a phase that combines volume-law entanglement and long-range correlations with fast, system-size-independent purification of an ancilla qubit and complete absence of scrambling. They reach this conclusion by mapping the averaged entanglement entropy to a two-dimensional statistical mechanics model whose continuous-time limit is an effective long-range XX Hamiltonian, placing the observed transition at the boundary between a symmetry-broken phase and a critical XY phase.

Core claim

In single-basis long-range measurement-only Clifford circuits there exists a dynamical phase in which volume-law and long-range entanglement coexist with rapid, size-independent purification of an ancilla qubit together with the absence of scrambling, a combination not observed in the corresponding random-basis circuits or in typical unitary dynamics.

What carries the argument

The replica-based mapping of trajectory-averaged entanglement entropy to a two-dimensional statistical mechanics model whose continuous-time limit produces an effective long-range XX Hamiltonian whose symmetry phases locate the entanglement transitions.

If this is right

  • The volume-law to sub-volume-law entanglement transition maps directly onto the boundary between a continuous symmetry broken phase and a critical XY phase in the effective long-range XX model.
  • Structured single-basis circuits allow preparation of highly entangled states that also purify an ancilla rapidly and without scrambling.
  • Probes such as mutual information, tripartite mutual information, and Bell-cluster statistics are required to distinguish the phases beyond entanglement entropy alone.
  • The same mapping and phase structure apply to both random-basis and single-basis protocols, with the latter revealing additional non-scrambling behavior.

Where Pith is reading between the lines

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

  • The reported phase supplies a concrete route to generate long-range entangled states for quantum sensing or metrology while keeping ancilla qubits clean.
  • Absence of scrambling in this regime may allow the circuits to preserve logical information in a manner useful for measurement-based error correction.
  • Tuning the measurement range or layer density further could uncover additional phases with controlled information flow.
  • The effective long-range XX description suggests analogous entanglement transitions may appear in other long-range interacting spin systems.

Load-bearing premise

The replica mapping to a statistical mechanics model together with the continuous-time limit to a long-range XX Hamiltonian accurately reproduces the steady-state entanglement properties without extra fitting parameters that would shift the phase boundaries.

What would settle it

A simulation in which the ancilla purification time grows with system size or in which tripartite mutual information shows scrambling signatures inside the reported volume-law regime would falsify the claimed phase.

Figures

Figures reproduced from arXiv: 2604.22022 by Abigail McClain Gomez, Ceren B. Da\u{g}, Fiona Abney-McPeek, Hong-Ye Hu, Susanne F. Yelin.

Figure 1
Figure 1. Figure 1: Overview of the central results. 1a The schematics of the phase diagrams for random-basis and single-basis circuit models with respect to measurement density and range obtained via Clifford circuit simulations. We obtain three and six different phases in random-basis and single-basis models, respectively. Each phase is depicted with a unique combination of scrambling, entanglement entropy, mutual informati… view at source ↗
Figure 2
Figure 2. Figure 2: 2a The long-range measurement-only circuit setup in our Clifford circuit simulations. The entire circuit is di￾vided into four equal subsystems, named from A to D. The circuit depth is depicted with a timeline marked by t on the left. A circuit layer is a time step where M2 many measure￾ments are performed, and the circuit density in this schematic is M2/N = 2/16 = 1/8. In the random-basis measurement mode… view at source ↗
Figure 3
Figure 3. Figure 3: Phase diagrams for random-basis measurement [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Here we examine six points across the random-basis phase diagram, as indicated by the matching marker and marker [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Steady state values of tripartite mutual information [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Time to steady state of tripartite mutual infor [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Here we consider six points across the parameter space, as indicated by the matching marker and marker color in Fig. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Projective XXZ model. Steady state values for TMI, mutual information, and entanglement entropy as a function of [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Phase diagrams for single-basis measurement [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Here we examine four points across the single-basis phase diagram, as indicated by the matching marker and marker [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Steady state values of tripartite mutual informa [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Observed values of I3, I (12a), and S (12b) for a single circuit trajectory at six points across the random-basis phase diagram, as indicated by the matching marker and marker color in [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Observed values of I3, I (13a), and S (13b) for a single circuit trajectory at four points across the single-basis phase diagram, as indicated by the matching marker and marker color in [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The effect of simulation depth. In the left panel, [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: 15a: Steady state values of tripartite mutual information and entanglement entropy vs interaction range parameter α for three values of circuit density M2/N and N ranging from 64 (lightest curves) to 512 (darkest curves). Entropy values are weighted by log N to highlight the regions of critical entanglement growth for M2/N = 0.0, 0.2, where the curves collapse on each other. The curves of I¯3 similarly ap… view at source ↗
Figure 16
Figure 16. Figure 16: 16a: Steady state values of tripartite mutual information and entanglement entropy vs interaction range parameter α for two values of circuit density M2/N and N ranging from 64 (lightest curves) to 512 (darkest curves). Entropy values are weighted by log N to highlight the regions of critical entanglement growth for M2/N = 0.2, 0.5, where the curves collapse on each other. The curves of I¯3 similarly appe… view at source ↗
read the original abstract

Measurement-only circuits provide a minimal setting in which repeated local projections can either generate or suppress many-body entanglement, giving rise to measurement-induced phase transitions and dynamical regimes, that might have no unitary counterpart. Here we investigate entanglement and information transitions in one-dimensional measurement-only Clifford circuits with long-range two-qubit parity checks. By tuning both the measurement range and density per layer, we uncover a broad set of phases whose classification requires probes beyond entanglement entropy, such as mutual information, tripartite mutual information, purification from an ancilla, and Bell-cluster statistics. We map phase diagrams using large-scale Clifford simulations for two protocols: a random-basis design in which each measurement is randomly chosen from $\lbrace XX,YY,ZZ \rbrace$, and a single-basis design in which the basis is fixed within each layer but varies between layers, hence introducing more structure to the circuit. We map the trajectory-averaged entanglement entropy to a two-dimensional statistical mechanics model by extending a replica-based method to random-basis measurement-only circuits, and show that a continuous-time limit yields an effective long-range XX hamiltonian in the steady state. This connection links the observed volume-law to sub-volume-law entanglement transition to the boundary between a continuous symmetry broken phase and a critical XY phase. Strikingly, in structured (single-basis) circuits we find a phase in which volume-law and long-range entanglement coexists with rapid, size-independent purification of an ancilla qubit, and the absence of scrambling, highlighting measurement-only circuits as a promising route to efficiently preparing highly entangled and technologically useful quantum states.

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

0 major / 3 minor

Summary. The manuscript investigates entanglement and information transitions in one-dimensional long-range measurement-only Clifford circuits by tuning measurement range and density per layer. It considers two protocols: a random-basis design with measurements randomly chosen from {XX, YY, ZZ} and a single-basis design with fixed basis per layer but varying across layers. Large-scale Clifford simulations map the phases using diagnostics including mutual information, tripartite mutual information, ancilla purification dynamics, and Bell-cluster statistics. For the random-basis protocol, the trajectory-averaged entanglement entropy is mapped to a two-dimensional statistical mechanics model via an extended replica method, with a continuous-time limit yielding an effective long-range XX Hamiltonian that links the volume-law to sub-volume-law transition to the boundary between a continuous symmetry broken phase and a critical XY phase. In the single-basis protocol, the authors report a phase in which volume-law and long-range entanglement coexist with rapid, size-independent ancilla purification and absence of scrambling.

Significance. If the numerical observations hold, the work is significant for identifying a structured measurement-only regime that generates volume-law entangled states while enabling fast purification without scrambling, offering a promising route to preparing technologically useful quantum states. The replica extension and continuous-time limit provide a theoretical connection between the observed transitions and statistical mechanics phases with broken symmetry. The manuscript is strengthened by its large-scale Clifford simulations and use of multiple independent probes (mutual information, tripartite mutual information, purification dynamics, and Bell-cluster statistics) to classify phases beyond entanglement entropy alone. The mapping to the 2D stat-mech model is applied only to the random-basis protocol and is not invoked for the central single-basis phase claim.

minor comments (3)
  1. Figure captions and methods sections should explicitly state the number of trajectories averaged, system sizes simulated, and any data exclusion criteria to allow assessment of statistical reliability of the reported phase boundaries.
  2. Clarify the precise definition and normalization of the 'measurement density per layer' parameter when tuning the phase diagrams, including how it interacts with the long-range measurement range.
  3. The abstract would benefit from briefly noting the specific diagnostics (beyond entanglement entropy) used to identify the absence of scrambling in the single-basis phase.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript and for recommending minor revision. We appreciate the recognition of the significance of the structured single-basis phase and the value of the multiple numerical probes employed. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; central claims rest on direct simulation diagnostics

full rationale

The paper's strongest claims concern numerically observed phases in single-basis long-range measurement-only Clifford circuits, supported by large-scale simulations with independent probes (mutual information, tripartite mutual information, ancilla purification dynamics, Bell-cluster statistics). The replica-based mapping to a 2D stat-mech model and continuous-time limit to an effective long-range XX Hamiltonian are explicitly restricted to interpreting the random-basis entanglement transition and are not invoked for the single-basis phase or its coexistence of volume-law entanglement with size-independent purification. No load-bearing step reduces by construction to fitted parameters, self-citations, or ansatz smuggling; the derivation chain remains self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Limited to abstract; the work assumes standard properties of Clifford circuits for efficient simulation and that the chosen entanglement and information probes suffice to classify all phases. No new entities are postulated.

free parameters (1)
  • measurement range and density per layer
    Tuned to uncover and map the phase diagrams in both random-basis and single-basis protocols.
axioms (1)
  • domain assumption Clifford circuits and replica trick extension accurately represent the entanglement dynamics of the measurement-only model
    Invoked to justify large-scale simulations and the mapping to the 2D statistical mechanics model.

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Reference graph

Works this paper leans on

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