REVIEW
Typicality of entanglement growth and transport fluctuations in quantum symmetric exclusion processes
Statistical Mechanics · Submitted 26 Oct 2026 · 83 references
Pith's verdict: Genuine advance with a real new mapping, and likely correct, but the universal almost-sure claim is conditional on an unproved saddle-uniqueness assumption; refereeing it is the right call.
T0 · AI review
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Referee report
The paper
The paper claims
The paper establishes that almost every noise realization of the quantum symmetric exclusion process has the same long-time charge-transfer statistics as the classical exclusion process, and that entanglement growth is thereby…
The reading
What carries the argument
Three pieces carry the argument. The forward–inverse moment comparison is the central object: the forward noise average $\mathbb{E}_W Z_W$ equals the SSEP expectation exactly (Eq. 13), while the inverse average is represented through a Gaussian integral over complex amplitudes whose squared moduli evolve autonomously, giving the exact equality to a Brownian energy process (BEP) expectation with independent exponential initial energies (Eq. 21). The load-bearing identity is the hydrodynamic field transformation $n = \varepsilon(1-p)$, $\pi = \log(1-p)$, previously used for the classical KMP energy model and SSEP, which maps the BEP Hamiltonian to $-H_{\mathrm{SSEP}}$ and maps the initial and final boundary functionals of the two MFT problems onto one another, so $S_{\mathrm{BEP}}\big|_{\mathrm{saddle}} = -S_{\mathrm{SSEP}}\big|_{\mathrm{saddle}}$; matched large-deviation exponents follow without solving the saddle equations. Finally, a locality upgrade converts convergence in probability into almost-sure convergence: only hopping across the cut enters the stochastic dynamics of $Z_W$, with uniformly bounded coefficients, so $e^{-c_z t}Z_W$ and $e^{-c_z t}Z_W^{-1}$ are supermartingales, and the maximal inequality for supermartingales together with the Borel–Cantelli lemma bounds all late-time deviations for a fixed realization. Entanglement enters through the free-fermion identity expressing Rényi entropies as combinations of the charge-transfer CGF at imaginary counting fields, extended from the real axis by a Vitali–Hurwitz analytic-continuation argument.
Extended reading notes
Core claim
The central claim is the almost-sure limit of Eq. (8): for any occupation-diagonal product initial state $\rho'_0$, every real counting field $z$, and $1 \ll \sqrt{Dt} \ll L$, the rescaled charge-transfer cumulant generating function $\kappa_W(z,t;\rho'_0)/\sqrt{Dt}$ converges to $\mu_{\mathrm{SSEP}}(z;\rho'_0)$, the scaled SSEP charge-transfer CGF. The forward noise average $\mathbb{E}_W Z_W$ equals the SSEP expectation exactly, because the noise-averaged QSSEP dynamics of occupation-diagonal states is classical SSEP. The inverse average requires the paper's main technical step: a Gaussian integral representation turns $\mathbb{E}_W Z_W^{-1}$ into an expectation of the classical Brownian energy process with independent exponential initial energies, and the field transformation $n = \varepsilon(1-p)$, $\pi = \log(1-p)$ maps that process's MFT action, boundary functionals included, to minus the SSEP action, so the on-shell actions are opposite and the forward and inverse large-deviation exponents match. Markov's inequality turns the matched exponents into convergence in probability, and a locality argument — only the bond across the cut changes $Z_W$, making $e^{-c_z t}Z_W$ and its inverse supermartingales — upgrades this to almost-sure convergence at all sufficiently late times. Analytic continuation to the imaginary counting fields needed for Rényi entropies follows from positivity and a bound on single-particle transmission across the cut, and a finite-time diffusion bound controls the von Neumann entropy integral.
Load-bearing premise
The derivation rests on the macroscopic fluctuation theory assumption, stated in the text as standard rather than proved for this model, that the dominant saddle point of the action at a finite counting field is smoothly connected to the zero-tilt hydrodynamic solution: if a dynamical phase transition to a competing saddle occurs, the matched large-deviation exponents of the forward and inverse moments no longer force the almost-sure limit, and the central claim could fail for those counting fields.
Editorial extensions
If this is right
- A single noise realization of QSSEP is representative: its rescaled charge-transfer CGF obeys the classical SSEP limit almost surely, for equilibrium states and for quenches from any occupation-diagonal product initial state (Eq. 8).
- Entanglement growth becomes self-averaging: Rényi and von Neumann entropies of a half-chain grow as $s_m\sqrt{Dt}+o(\sqrt{Dt})$ in individual runs, with coefficients $(s_1,s_2,s_3) \simeq (0.5238,0.4141,0.3729)$ for a domain wall and $(0.6363,0.4986,0.4479)$ for a Néel state.
- The subsystem covariance eigenvalue distribution becomes deterministic: the rescaled cumulative eigenvalue count converges to $N_{\mathrm{DW}}(\nu) = \frac{2}{\pi}\sqrt{-\log\nu}$ for a domain wall and to $N_{\mathrm{N\'eel}}(\nu) = \frac{\sqrt{2}}{\pi}\,\mathrm{sgn}(\frac{1}{2}-\nu)\sqrt{-\log[4\nu(1-\nu)]}$ for a Néel state.
- Typicality holds beyond the real axis: analytic continuation to the strip $|\mathrm{Im}\,z| < \pi$ covers all integer Rényi entropies, and a finite-time diffusion bound covers the von Neumann entropy integral.
- The result moves typicality of charge-transfer statistics from the stationary boundary-driven regime studied previously to transient fluctuations in the thermodynamic limit.
Reading between the lines
- The forward–inverse moment comparison reads like a general recipe: for any diffusive quantum model whose noise-averaged dynamics is a classical process, proving typicality reduces to representing the inverse moment as another classical process with a tractable MFT action. A natural test is a two-dimensional QSSEP-like model, where the field transformation has not yet been shown to hold.
- If the covariance eigenvalue distribution self-averages, finer observables of the same Gaussian state — the full entanglement spectrum and the subsystem particle-number distribution at fixed counting field — should also be typical in single runs. That is a testable consequence the paper does not spell out.
- The proof's deviation bound — probability of a finite error suppressed like $e^{-\varepsilon\sqrt{Dt}}$ — doubles as a quantitative timescale: it says how long a single noisy quantum-simulator run must last before its measured entropy curve locks onto the $s_m\sqrt{Dt}$ form.
- The acknowledged saddle-connection assumption marks the boundary of the claim: at large counting fields, where rare large charge transfers dominate, a dynamical phase transition could break typicality. Locating the largest $z$ at which the empirical CGF still matches $\mu_{\mathrm{SSEP}}(z)$ would map the actual regime of validity.
Original abstract
We use macroscopic fluctuation theory (MFT) to establish the typicality of charge-transfer statistics and entanglement dynamics in the quantum symmetric exclusion process, a model of stochastically hopping free fermions with diffusive transport and long-range quantum coherence. We show that the leading long-time charge-transfer full counting statistics of individual noise realizations coincide almost surely with those of the classical symmetric exclusion process (SSEP), in equilibrium and following quenches from arbitrary occupation-diagonal product states. Our results apply to transient fluctuations in the thermodynamic limit, extending previous work that has primarily focused on stationary regimes. Our approach compares the noise averages of the charge-transfer generating function and its inverse. The former reduces to SSEP, while the latter maps to an auxiliary Brownian energy process whose MFT saddle-point problem is related to that of SSEP, yielding matching large-deviation exponents. Through free-fermion identities relating entanglement to subsystem-number fluctuations, this establishes the self-averaging of the covariance-matrix eigenvalue distribution and of R\'enyi and von Neumann entropies. We obtain asymptotically exact predictions for entanglement growth from domain-wall and N\'eel initial states, in excellent agreement with numerical simulations.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We use macroscopic fluctuation theory (MFT) to establish the typicality of charge-transfer statistics and entanglement dynamics in the quantum symmetric exclusion process, a model of stochastically hopping free fermions with diffusive transport and long-range quantum coherence. We show that the leading long-time charge-transfer full counting statistics of individual noise realizations coincide almost surely with those of the classical symmetric exclusion process (SSEP), in equilibrium and following quenches from arbitrary occupation-diagonal product states. Our results apply to transient fluctuations in the thermodynamic limit, extending previous work that has primarily focused on stationary regimes. Our approach compares the noise averages of the charge-transfer generating function and its inverse. The former reduces to SSEP, while the latter maps to an auxiliary Brownian energy process whose MFT saddle-point problem is related to that of SSEP, yielding matching large-deviation exponents. Through free-fermion identities relating entanglement to subsystem-number fluctuations, this establishes the self-averaging of the covariance-matrix eigenvalue distribution and of R\'enyi and von Neumann entropies. We obtain asymptotically exact predictions for entanglement growth from domain-wall and N\'eel initial states, in excellent agreement with numerical simulations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use macroscopic fluctuation theory (MFT) to establish the typicality of charge-transfer statistics and entanglement dynamics in the quantum symmetric exclusion process, a model of stochastically hopping free fermions with diffusive transport and long-range quantum coherence. | contribution 0.95 | 0.93 | 0.73 | asserted 1.00 |
| s1 | We show that the leading long-time charge-transfer full counting statistics of individual noise realizations coincide almost surely with those of the classical symmetric exclusion process (SSEP), in equilibrium and following quenches from arbitrary occupation-diagonal product states. | result 1.00 | 0.94 | 0.48 | asserted 1.00 |
| s2 | Our results apply to transient fluctuations in the thermodynamic limit, extending previous work that has primarily focused on stationary regimes. | gap 0.48 | 0.78 | 0.07 | asserted 1.00 |
| s3 | Our approach compares the noise averages of the charge-transfer generating function and its inverse. | method 0.99 | 0.89 | 0.04 | asserted 0.96 |
| s4 | The former reduces to SSEP, while the latter maps to an auxiliary Brownian energy process whose MFT saddle-point problem is related to that of SSEP, yielding matching large-deviation exponents. | method 0.97 | 0.88 | 0.09 | asserted 1.00 |
| s5 | Through free-fermion identities relating entanglement to subsystem-number fluctuations, this establishes the self-averaging of the covariance-matrix eigenvalue distribution and of R\'enyi and von Neumann entropies. | result 0.86 | 0.92 | 0.22 | asserted 1.00 |
| s6 | We obtain asymptotically exact predictions for entanglement growth from domain-wall and N\'eel initial states, in excellent agreement with numerical simulations. | result 1.00 | 0.96 | 0.20 | asserted 1.00 |
What was examined, and what was not
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Discussion
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