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arxiv: 2604.10315 · v1 · submitted 2026-04-11 · 🪐 quant-ph

Comparing quantum and classical finite state generators

Prasenjit Deb , Almut Beige , Lewis A. Clark This is my paper

Pith reviewed 2026-05-10 15:40 UTC · model grok-4.3

classification 🪐 quant-ph
keywords temporal correlationsBell-CHSH inequalityTsirelson boundquantum finite state generatorsclassical vs quantumstochastic processestime delay
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The pith

Classical stochastic generators can exceed the Tsirelson bound in temporal correlations while quantum ones preserve them longer with delays.

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

The paper demonstrates that Bell-CHSH-like inequalities, effective for spatial quantum correlations, are insufficient for benchmarking temporal correlations. It parametrizes simple classical generators using a single bit and quantum ones using a single qubit, then compares their output sequences under sequential measurements. Classical machines are found to surpass the Tsirelson bound of 2√2 due to their structure. Introducing time delays between measurements shows quantum machines maintaining correlations longer against scrambling operations. This provides a way to distinguish quantum from classical temporal processes.

Core claim

For sequential measurements by Alice and Bob, classical machines can exceed the Tsirelson bound of 2√2 in a Bell-CHSH-like inequality applied to temporal correlations from their output sequences. When a time delay is considered between consecutive measurements, quantum machines based on a qubit can outperform classical ones by maintaining correlations longer under generally scrambling operations.

What carries the argument

Stochastic finite state generators parametrized by a single bit for classical and a single qubit for quantum, with their temporal output correlations tested via a Bell-CHSH-like inequality.

If this is right

  • Classical finite state generators can produce stronger temporal correlations than the quantum Tsirelson bound allows in no-delay scenarios.
  • Quantum generators provide an advantage in preserving correlations over time delays under scrambling.
  • The distinction allows identification of quantum resources in temporal correlation tasks.
  • Bell inequalities need modification or supplementation for effective benchmarking of temporal quantum effects.

Where Pith is reading between the lines

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

  • Such comparisons could inform designs for quantum technologies relying on time-based correlations, like in quantum memory or communication protocols.
  • Generalizing to multi-bit or multi-qubit generators might uncover additional quantum advantages or classical limits.
  • Experimental implementations with delayed measurements could test these distinctions in real systems.

Load-bearing premise

The parametrization of classical and quantum stochastic finite state generators based on a single bit and a single qubit respectively is sufficient to capture the general behavior of temporal correlations in such systems.

What would settle it

An experiment measuring the correlation values in sequential measurements with and without time delays for single-bit classical and single-qubit quantum generators, checking if classical exceeds 2√2 without delay and if quantum shows superior maintenance with delay.

Figures

Figures reproduced from arXiv: 2604.10315 by Almut Beige, Lewis A. Clark, Prasenjit Deb.

Figure 1
Figure 1. Figure 1: Schematic diagram of the scenario that we consider [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: CHSH scores of 1-bit HMMs, 1-qubit HQMMs and [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: CHSH scores for the three classifications of machines, again sampled from 10 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

Bell-CHSH-like inequalities have been very successful in benchmarking {\it spatial} quantum correlations. However, as this paper illustrates, they are in general not sufficient for benchmarking {\it temporal} quantum correlations. To show this, we parametrise classical and quantum stochastic finite state generators based on a single bit and a single qubit, respectively, and compare the temporal correlations of their output sequences using a Bell-CHSH-like inequality. We find that for sequential measurements by two observers, Alice and Bob, classical machines can exceed the Tsirelson bound of $2\sqrt{2}$, due to their fundamental structure. However, when we consider a time delay between consecutive measurements, we find examples where the quantum machines outperform their classical counterparts by maintaining correlations longer under generally scrambling operations. Our result can be used to distinguish quantum from classical processes and to identify novel resources for quantum technology applications.

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 / 1 minor

Summary. The manuscript parametrizes classical stochastic finite state generators with a single bit and quantum generators with a single qubit. It applies a Bell-CHSH-like inequality to the temporal correlations in output sequences generated under sequential measurements by two observers. The central claims are that classical generators can exceed the Tsirelson bound of 2√2 owing to their structure, while the introduction of a time delay between measurements yields cases in which the quantum generators maintain correlations longer under scrambling operations. The results are presented as a means to distinguish quantum from classical processes and to identify resources for quantum technology.

Significance. If the comparative advantage under time delay holds, the work supplies concrete, low-dimensional examples showing that spatial Bell-CHSH inequalities are insufficient for temporal correlations and offers a practical diagnostic for quantum versus classical stochastic processes. The explicit single-bit and single-qubit constructions constitute a strength, as they allow direct, reproducible comparison of correlation decay.

major comments (2)
  1. [Parametrization and comparison sections] The central distinction between classical and quantum performance rests on the single-bit and single-qubit parametrizations. No argument or additional example is supplied showing that these minimal cases are representative; if higher-dimensional generators reverse the observed ordering (classical no longer exceeds 2√2 or quantum advantage disappears), the utility for distinguishing processes does not follow.
  2. [Results on time-delayed correlations] The application of the Bell-CHSH-like inequality to delayed measurements requires an explicit definition of the scrambling operations and the precise form of the correlation function (including how the time delay enters the generator evolution). Without these, it is impossible to verify that the reported quantum outperformance is not an artifact of the chosen parametrization.
minor comments (1)
  1. [Abstract] The abstract refers to 'generally scrambling operations' without a brief definition or reference to the section where they are formalized.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us clarify the scope and presentation of our results. We address each major comment below and have revised the manuscript accordingly to improve clarity and address the concerns raised.

read point-by-point responses

  1. Referee: [Parametrization and comparison sections] The central distinction between classical and quantum performance rests on the single-bit and single-qubit parametrizations. No argument or additional example is supplied showing that these minimal cases are representative; if higher-dimensional generators reverse the observed ordering (classical no longer exceeds 2√2 or quantum advantage disappears), the utility for distinguishing processes does not follow.

    Authors: We acknowledge that the manuscript centers on the minimal single-bit and single-qubit parametrizations without an explicit argument for their representativeness in higher dimensions. These cases were selected because they permit complete analytical computation of the correlation functions and enable a direct, reproducible comparison between classical and quantum generators. The key insight is that even these simplest non-trivial generators already demonstrate that classical machines can exceed the Tsirelson bound in temporal correlations (due to the structure of stochastic finite-state machines) and that quantum generators can maintain correlations longer under time delays. The paper does not assert that this ordering holds universally across all dimensions; rather, it provides concrete low-dimensional examples showing that spatial Bell-CHSH inequalities are insufficient for temporal correlations and that such distinctions can serve as a diagnostic. To address the referee's concern, we have added a paragraph in the introduction and a note in the conclusions clarifying that the results are illustrative for minimal dimensions and that investigating higher-dimensional generators remains an open direction for future work. revision: yes

  2. Referee: [Results on time-delayed correlations] The application of the Bell-CHSH-like inequality to delayed measurements requires an explicit definition of the scrambling operations and the precise form of the correlation function (including how the time delay enters the generator evolution). Without these, it is impossible to verify that the reported quantum outperformance is not an artifact of the chosen parametrization.

    Authors: We thank the referee for highlighting this point. The scrambling operations are defined in Section III as the application of random unitary (or stochastic) maps to the internal state between successive measurements, and the correlation function is given in Equation (5) as the two-time expectation value ⟨A B⟩ with the time delay τ incorporated through the generator's evolution operator applied for τ steps. For the quantum case this is the unitary evolution of the qubit state; for the classical case it is the corresponding Markov transition matrix raised to the power τ. We apologize if these elements were not stated with sufficient prominence. In the revised manuscript we have added a dedicated subsection (new Section III.B) that restates the definitions explicitly, provides the precise mathematical forms for both classical and quantum generators, and shows how the delay enters the correlation function. This should allow full verification that the reported quantum advantage under delay is not an artifact. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper explicitly defines parametrizations for single-bit classical and single-qubit quantum stochastic finite state generators, then computes temporal correlations via a Bell-CHSH-like inequality on output sequences. The observation that classical models exceed 2√2 follows directly from the defined structure under sequential measurements, without any reduction of the result to a fitted parameter, self-definition, or self-citation chain. No ansatz is smuggled, no known result is merely renamed, and the comparison remains self-contained within the chosen minimal models. The derivation does not collapse to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that minimal single-bit classical and single-qubit quantum generators adequately represent temporal correlation behaviors, along with standard quantum mechanics for operations and measurements.

axioms (2)
  • domain assumption Single bit and single qubit models suffice to represent general classical and quantum stochastic finite state generators for temporal correlations
    The paper bases its comparison and conclusions on these specific minimal models.
  • domain assumption Bell-CHSH-like inequality applies directly to temporal output sequences from sequential measurements
    The inequality is extended from spatial to temporal settings without additional justification in the abstract.

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