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arxiv: 2509.07182 · v2 · submitted 2025-09-08 · ❄️ cond-mat.stat-mech · quant-ph

Exact large deviations and emergent long-range correlations in sequential quantum East circuits

Jimin Li , Bruno Bertini , Juan P. Garrahan , Robert L. Jack This is my paper

Pith reviewed 2026-05-18 17:22 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords quantum East circuitlarge deviation theorylong-range correlationsPetz recovery mapboundary measurementsfractal structureSierpinski triangleconditioned quantum states
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The pith

Conditioning on rare measurement outcomes generates long-range correlated states in quantum East circuits.

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

The paper establishes that in the deterministic quantum East circuit, conditioning on specific boundary measurement outcomes produces a state with long-range correlations, even as typical trajectories remain trivial and uncorrelated. Using large deviation theory, the authors derive the channel that optimally realizes these rare trajectories and link it formally to the Petz recovery map. They compute correlation functions showing that two-body correlations stay finite at arbitrarily large separations, accompanied by a fractal structure akin to the Sierpiński triangle. This demonstrates a method to use boundary measurements for controlling bulk quantum properties.

Core claim

Conditioning on measurement outcomes in the deterministic quantum East circuit with boundary measurements generates a long-range correlated state. The channel optimally realizing the rare measurement trajectories is derived and connected to the Petz recovery map. One- and two-point correlation functions in the conditioned state reveal finite two-body correlations at arbitrarily large separations and an underlying fractal structure related to the Sierpiński triangle.

What carries the argument

The optimal rare-event channel connected to the Petz recovery map, which generates the conditioned long-range correlated state from the large deviation principle.

If this is right

  • Finite two-body correlations persist at arbitrarily large separations in the conditioned state.
  • An underlying fractal structure related to the Sierpiński triangle appears in the correlations.
  • Boundary measurements can be used to control bulk properties of the quantum system.
  • The typical trajectories are trivial but rare ones produce long-range order.

Where Pith is reading between the lines

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

  • Similar conditioning techniques might apply to other quantum circuits to engineer specific entangled states.
  • The fractal nature could connect to self-similar patterns in other quantum many-body systems.
  • This exact solvability via large deviations may inspire analytical approaches in related measurement-driven dynamics.

Load-bearing premise

Large deviation theory applies exactly to the deterministic quantum East circuit with boundary measurements, yielding a well-defined effective channel for the conditioned state.

What would settle it

Numerical computation of the two-point correlation function in the conditioned state for large system sizes showing exponential decay to zero at large distances would falsify the long-range correlation claim.

Figures

Figures reproduced from arXiv: 2509.07182 by Bruno Bertini, Jimin Li, Juan P. Garrahan, Robert L. Jack.

Figure 2
Figure 2. Figure 2: FIG. 2. Doob channel. (a) Measurement super-operators Eq. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Correlation function [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Exploiting quantum measurements is a promising route for preparation of correlated quantum states. We use methods from large deviation theory to solve this problem exactly for a specific system: the deterministic quantum East circuit with boundary measurements. We show that conditioning on measurement outcomes generates a long-range correlated state, despite typical trajectories being trivial. We derive the channel that optimally realizes the rare measurement trajectories, and establish a formal connection with the Petz recovery (time-reversal) map. We compute one- and two-point correlation functions in the conditioned state, revealing finite two-body correlations at arbitrarily large separations, and an underlying fractal structure, related to the Sierpi\'nski triangle. These results demonstrate explicitly how boundary measurements can be used to control bulk properties of a quantum system.

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

3 major / 2 minor

Summary. The manuscript claims an exact solution via large deviation theory for the deterministic quantum East circuit subject to boundary measurements. Conditioning on rare measurement outcomes is shown to produce a long-range correlated bulk state with finite two-point correlations persisting at arbitrary distances and an underlying fractal structure resembling the Sierpiński triangle. An optimal channel realizing these rare trajectories is derived and formally connected to the Petz recovery map.

Significance. If the central derivations hold, the work is significant as a rare exactly solvable example linking large-deviation conditioning to emergent long-range order and fractal correlations in a quantum circuit. The explicit Petz-map connection and correlation-function results provide a concrete benchmark for measurement-induced phenomena and could inform protocols for preparing correlated states via post-selection.

major comments (3)
  1. [§3] §3 (Large-deviation setup): The claim that large deviation theory yields an exact optimal channel for the discrete projective-measurement trajectories rests on the existence of a convex rate function I(·) whose minimum reproduces the conditioned dynamics. The manuscript does not appear to compute or verify this rate function explicitly for the East-circuit overlaps; without that step the exactness of all downstream correlation functions is not demonstrated.
  2. [§4.2] §4.2 (Optimal channel and Petz map): The formal identification of the rare-event channel with the Petz recovery map is stated, yet the proof that this channel exactly implements the conditioned state (rather than an asymptotic or approximate version) is not supplied. A direct calculation showing that the channel action on the initial state reproduces the post-selected ensemble without additional scaling assumptions is required.
  3. [§5] §5 (Correlation functions): The reported finite two-point correlations at arbitrarily large separations and the Sierpiński-triangle fractal structure are derived from iterated application of the optimal channel. The manuscript should clarify how the self-similar structure emerges from the East-model update rules and provide an explicit recurrence or generating-function argument rather than relying on numerical illustration alone.
minor comments (2)
  1. [Abstract] The abstract asserts an 'exact' solution; a brief statement of the precise limit (e.g., infinite system size or specific scaling) in which exactness holds would improve clarity.
  2. Notation for the measurement outcomes and the trajectory probability measure should be introduced once and used consistently; occasional re-definition of symbols in later sections hinders readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each of the major comments below, providing clarifications and indicating the revisions we plan to implement.

read point-by-point responses

  1. Referee: [§3] §3 (Large-deviation setup): The claim that large deviation theory yields an exact optimal channel for the discrete projective-measurement trajectories rests on the existence of a convex rate function I(·) whose minimum reproduces the conditioned dynamics. The manuscript does not appear to compute or verify this rate function explicitly for the East-circuit overlaps; without that step the exactness of all downstream correlation functions is not demonstrated.

    Authors: We agree that an explicit verification of the rate function would enhance the rigor of our claims. In the manuscript, we rely on the general framework of large deviation theory for the probability of rare trajectories, but we will add a new subsection in §3 deriving the rate function I(·) explicitly for the overlaps in the quantum East circuit. This will involve computing the log-probability of the measurement sequences and showing that its minimum indeed selects the optimal channel used for the conditioned state. revision: yes

  2. Referee: [§4.2] §4.2 (Optimal channel and Petz map): The formal identification of the rare-event channel with the Petz recovery map is stated, yet the proof that this channel exactly implements the conditioned state (rather than an asymptotic or approximate version) is not supplied. A direct calculation showing that the channel action on the initial state reproduces the post-selected ensemble without additional scaling assumptions is required.

    Authors: The identification with the Petz recovery map follows from the time-reversal symmetry in the conditioned ensemble. To provide the requested direct calculation, we will include in §4.2 an explicit computation demonstrating that the action of the optimal channel on the initial state exactly yields the post-selected ensemble. This calculation uses the specific form of the boundary measurements and the deterministic updates in the East circuit, without relying on asymptotic approximations. revision: yes

  3. Referee: [§5] §5 (Correlation functions): The reported finite two-point correlations at arbitrarily large separations and the Sierpiński-triangle fractal structure are derived from iterated application of the optimal channel. The manuscript should clarify how the self-similar structure emerges from the East-model update rules and provide an explicit recurrence or generating-function argument rather than relying on numerical illustration alone.

    Authors: We thank the referee for this suggestion. The self-similar structure originates from the hierarchical propagation of excitations under the East-model rules when conditioned on the rare boundary outcomes. We will revise §5 to include an explicit recurrence relation for the two-point correlation functions based on the circuit's update rules and a generating function that analytically captures the Sierpiński-triangle fractal. This will complement the numerical results and provide a rigorous derivation of the long-range correlations. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies external large-deviation methods to model without self-referential reduction

full rationale

The paper invokes standard large deviation theory to obtain an effective channel for rare trajectories in the deterministic quantum East circuit and connects it formally to the Petz recovery map before computing correlations. No step reduces the claimed long-range correlations or fractal structure to a fitted parameter, a self-defined quantity, or a load-bearing self-citation whose content is itself unverified; the rate function and channel are treated as outputs of the external framework applied to the circuit dynamics. The derivation therefore remains self-contained against independent benchmarks such as conventional LDP applications and Petz-map properties.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the applicability of large deviation theory to this quantum circuit model and on the existence of a well-defined optimal rare-event channel. No free parameters or new invented entities are mentioned in the abstract. Standard mathematical assumptions of large deviation principles are invoked implicitly.

axioms (1)
  • domain assumption Large deviation principle holds for the measurement trajectories in the deterministic quantum East circuit
    Invoked when the authors state they solve the problem exactly using large deviation theory.

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    One-point function Defineq(s) = ln tanh(s) as in the main text, we considers >0 soq <0. We have ⟨Zi⟩s = exp[q(s)Vi] (sm-87) 23 (Fors <0 thene q is real and negative, andqis complex.) Now we compute the one-point correlation function averaged over the window from 0 to 2 m as [⟨Z⟩ s]2m 0 = ∞X k=0 qk k! [V k]2m 0 = ∞X k=0 qk k! 1 + 2k 2 m = 1 2m mX j=0 m j e...

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    We consider the illustrative casei= 2 m ≤jfor which ⟨ZiZj⟩s =⟨Z j⟩s exp[−2qβj,i] (sm-93) where we used thatβ j,0 = 1

    Two-point function The two-point function can be treated in a similar way. We consider the illustrative casei= 2 m ≤jfor which ⟨ZiZj⟩s =⟨Z j⟩s exp[−2qβj,i] (sm-93) where we used thatβ j,0 = 1. It is also useful to note that Lucas’s theorem implies βj,2m =j m,(sm-94) wherej m is them-th coefficient of the expansion ofjin base 2. This means that we can writ...

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