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arxiv: 2504.20953 · v2 · submitted 2025-04-29 · 🪐 quant-ph

Optimal Local Simulations of a Quantum Singlet

David Llamas , Dmitry Chistikov , Adrian Kent , Mike Paterson , Olga Goulko This is my paper

Pith reviewed 2026-05-22 18:21 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Bell nonlocalitylocal hidden variablessinglet statespin modelsBell testsquantum correlationsanticorrelationsground state optimization
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The pith

Local hidden variable models for the quantum singlet at any fixed measurement angle can be found by computing ground states of fixed-range classical spin models.

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

The paper establishes a numerical method to determine the strongest anticorrelations that any local hidden variable model can achieve when two parties measure the singlet state along axes separated by a chosen fixed angle. It does this by converting the search for the optimal local model into the task of finding the lowest-energy configuration of a chain of classical spins whose interactions reach only a fixed distance along the chain. A reader would care because the size of the remaining gap to the quantum prediction determines how powerfully an experiment can demonstrate that no local model suffices, and because the largest gaps point to the measurement angles that make the strongest Bell tests. The authors then use the method to locate those angles where the classical-quantum difference is greatest.

Core claim

By mapping the problem of maximizing anticorrelations under local hidden variable models for fixed-angle projective measurements on the singlet onto the ground-state search for fixed-range spin models, the authors obtain the maximal classical anticorrelation value for every angle and thereby identify the angles that produce the largest gap to the quantum value.

What carries the argument

The mapping of maximal LHV anticorrelation for fixed-angle singlet measurements onto the ground-state energy minimization of a fixed-range classical spin model.

If this is right

  • The size of the quantum-classical anticorrelation gap becomes computable for every fixed angle.
  • Angles that maximize the gap are singled out as the most efficient choices for experimental Bell tests.
  • Bell nonlocality can be quantified more precisely as a resource whose strength varies with measurement angle.
  • The same reduction supplies a systematic way to compare local models across the full range of possible angles.

Where Pith is reading between the lines

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

  • The spin-model technique could be adapted to optimize local models for other two-qubit states or for measurements with more than two outcomes.
  • Experimental groups might pre-select the identified optimal angles to reduce the number of trials needed for a given violation strength.
  • Device-independent protocols in quantum cryptography could incorporate the angle-dependent gap sizes when estimating security margins.

Load-bearing premise

Finding the highest anticorrelation any local hidden variable model can produce for fixed-angle measurements on the singlet is exactly equivalent to finding the lowest energy of a corresponding fixed-range classical spin chain.

What would settle it

An explicit local hidden variable strategy that produces a higher anticorrelation than the ground-state energy of the associated spin model for the same angle would falsify the reduction.

Figures

Figures reproduced from arXiv: 2504.20953 by Adrian Kent, David Llamas, Dmitry Chistikov, Mike Paterson, Olga Goulko.

Figure 2
Figure 2. Figure 2: FIG. 2. The jump [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Labyrinth shapes around [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Probability of optimal lawn shapes as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

Bell's seminal work showed that no local hidden variable (LHV) model can fully reproduce the quantum correlations of a two-qubit singlet state. His argument and later developments by Clauser et al. effectively rely on gaps between the anticorrelations achievable by classical models and quantum theory for projective measurements along randomly chosen axes separated by a fixed angle. However, the size of these gaps has to date remained unknown. Here we numerically determine the LHV models maximizing anticorrelations for random axes separated by any fixed angle, by mapping the problem onto ground state configurations of fixed-range spin models. We identify angles where this gap is largest and thus best suited for Bell tests. These findings enrich the understanding of Bell non-locality as a physical resource in quantum information theory and quantum cryptography.

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 paper claims that the maximal classical anticorrelations achievable by LHV models for the singlet state under projective measurements separated by a fixed angle φ can be found by mapping the functional optimization over response functions to the ground-state energy of a classical fixed-range Ising spin model on a discretized sphere; the resulting numerical values are then used to identify the angles φ that maximize the gap to the quantum value −cos(φ), thereby pinpointing settings best suited for Bell tests.

Significance. If the numerical optima are shown to converge to the true continuous LHV bound, the work would supply concrete, angle-resolved classical limits that could directly inform the design of more sensitive Bell experiments and quantify nonlocality as a resource. The reduction of the infinite-dimensional optimization to a finite spin-model ground-state search is a technically interesting technique that may generalize to other correlation problems in quantum foundations.

major comments (2)
  1. [mapping paragraph] The section describing the mapping (paragraph beginning 'Here we numerically determine'): the reduction to ground-state energies of fixed-range spin models on a finite mesh yields only an upper bound on the true infimum of C(φ); no convergence analysis with respect to mesh refinement or error estimate as a function of φ is provided. Because the paper selects optimal angles from these discrete values, an uncontrolled φ-dependent discretization bias directly affects the reliability of the reported maximal-gap angles.
  2. [results] Results section (where angles maximizing the gap are identified): the post-hoc selection of angles relies on the numerical C_class(φ) values; without a demonstration that the location of the maximum remains stable under increased discretization density, the claim that certain angles are 'best suited for Bell tests' rests on potentially biased data.
minor comments (2)
  1. [methods] Notation: the definition of the measure μ_φ and the precise range of the spin-model couplings should be stated explicitly in the methods to allow independent reproduction.
  2. [figures] Figure captions: clarify whether the plotted curves show raw ground-state energies or the derived gaps, and indicate the mesh size used for each data point.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address each major comment below and indicate how we will revise the manuscript to strengthen the numerical analysis.

read point-by-point responses

  1. Referee: [mapping paragraph] The section describing the mapping (paragraph beginning 'Here we numerically determine'): the reduction to ground-state energies of fixed-range spin models on a finite mesh yields only an upper bound on the true infimum of C(φ); no convergence analysis with respect to mesh refinement or error estimate as a function of φ is provided. Because the paper selects optimal angles from these discrete values, an uncontrolled φ-dependent discretization bias directly affects the reliability of the reported maximal-gap angles.

    Authors: We agree that the finite-mesh mapping provides an upper bound to the true infimum of C(φ) and that the absence of a convergence study leaves open the possibility of φ-dependent bias. In the revision we will add an appendix presenting C_class(φ) and the resulting gaps for at least three successively refined meshes (doubling the number of discretization points each time). We will report the variation in the identified gap-maximizing angles across these meshes and supply a simple error estimate based on the difference between the two finest grids. revision: yes

  2. Referee: [results] Results section (where angles maximizing the gap are identified): the post-hoc selection of angles relies on the numerical C_class(φ) values; without a demonstration that the location of the maximum remains stable under increased discretization density, the claim that certain angles are 'best suited for Bell tests' rests on potentially biased data.

    Authors: We accept that stability of the maximizing angles must be demonstrated before the claim can be considered robust. The revised manuscript will include a short subsection (or supplementary figure) that recomputes the gap-maximizing angles on the refined meshes mentioned above. If the locations remain unchanged within the reported precision, we will retain the original angles; otherwise we will update them to the values obtained on the finest mesh and adjust the associated discussion accordingly. revision: yes

Circularity Check

0 steps flagged

No circularity in numerical mapping to spin-model ground states

full rationale

The paper reformulates the LHV anticorrelation maximization for fixed-angle measurements as a ground-state search in fixed-range classical spin models on a discretized sphere, then reports numerical results for the optimal values and the angles maximizing the gap to the quantum bound. This is a direct computational reduction to an external optimization task with no equations that define the reported maxima in terms of themselves, no fitted parameters from a data subset then relabeled as predictions, and no load-bearing self-citations or uniqueness theorems imported from prior author work. The central claims remain outputs of the numerical procedure rather than inputs by construction, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unproven equivalence between LHV maximization and classical spin ground-state search; no free parameters or new entities are declared in the abstract.

axioms (1)
  • domain assumption The maximum anticorrelation achievable by any LHV model for fixed-angle measurements equals the ground-state energy of a corresponding fixed-range classical spin model.
    This equivalence is invoked to justify the numerical approach (abstract).

pith-pipeline@v0.9.0 · 5660 in / 1194 out tokens · 45131 ms · 2026-05-22T18:21:05.018545+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Grasshopper Problem on the Sphere

    quant-ph 2026-03 unverdicted novelty 4.0

    The paper provides the detailed geometric and computational methods for solving the spherical grasshopper problem in the context of Bell inequalities and singlet simulation.

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