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arxiv: 2501.01434 · v2 · pith:BHZ2DCFInew · submitted 2024-12-18 · ⚛️ physics.ed-ph · quant-ph

Simulating Bell inequalities with Qibo

Isabella Masina , Giuseppe Lo Presti , Matteo Robbiati , Michele Grossi This is my paper

Pith reviewed 2026-05-23 07:21 UTC · model grok-4.3

classification ⚛️ physics.ed-ph quant-ph
keywords Bell inequalitiesquantum computingQiboentanglementnon-localityeducational materialquantum simulationclassroom modules
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0 comments X

The pith

Qibo supplies code and three-tier lesson plans to simulate Bell inequality violations in quantum circuits.

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

The paper supplies ready-to-run Qibo implementations and classroom guides that let students simulate the violation of Bell inequalities. The material is split into three modules that move from ideal cases to realistic noise, giving direct experience with entanglement, correlations, and the failure of local hidden-variable models. A reader would care because the approach turns abstract quantum foundations into executable code that also exposes statistical and hardware effects present on current devices.

Core claim

The authors present three modules of increasing difficulty, each containing Qibo code that implements Bell inequality tests on quantum circuits. These tools allow students to observe numerical violations, explore the role of hidden variables, and examine how statistical sampling and device noise modify the results.

What carries the argument

Qibo quantum-circuit implementations of Bell tests, structured as three progressive classroom modules that incorporate both ideal evolution and noise models.

If this is right

  • Students obtain executable examples that demonstrate explicit numerical violation of Bell inequalities.
  • The modules let learners add noise channels and observe how real-device imperfections reduce the observed violation.
  • Classroom time can be organized around concrete coding tasks rather than purely theoretical derivations.
  • The same framework supports both software simulation and direct calls to quantum hardware.

Where Pith is reading between the lines

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

  • The same modular structure could be reused for teaching other correlation-based quantum protocols such as quantum key distribution.
  • Extending the modules to include error-mitigation techniques would make the gap between ideal and hardware results even more visible.
  • An instructor could pair the Qibo notebooks with classical Monte-Carlo simulations to contrast the computational cost of reproducing the same statistics.

Load-bearing premise

The provided code and guides will actually help students understand entanglement and non-locality.

What would settle it

A controlled comparison in which students who complete the modules show no measurable gain in correctly identifying the incompatibility between quantum predictions and local hidden-variable theories compared with students taught only through lectures.

Figures

Figures reproduced from arXiv: 2501.01434 by Giuseppe Lo Presti, Isabella Masina, Matteo Robbiati, Michele Grossi.

Figure 1
Figure 1. Figure 1: Experimental setup to study the Bell-Wigner inequality. The system in the final state is assumed to be made of two spin-1/2 particles flying apart, say along the y direction, with null relative orbital angular momentum. The latter requirement is important as, due to angular momentum conservation, this implies that the particles still are in a total spin singlet state. Observers A (Alice) and B (Bob) measur… view at source ↗
Figure 2
Figure 2. Figure 2: Three directions for the experimental setup studying the Bell-Wigner inequality. Following Wigner [18], let us assume that some local hidden (LH) variable allows us to classify entangled pairs into various populations, according to the outcomes that A and B would find choosing to measure the spin along aˆ, ˆb or cˆ. In any given event, the pair must be a member of one of the eight populations shown in tabl… view at source ↗
Figure 3
Figure 3. Figure 3: QW QM is shown as a function of θac. Left: for selected values of ϕ and taking θab = π/2. Right: for selected values of θab and taking ϕ = 0. The maximal violation configuration (ϕ = 0, θac = π/4, θab = π/2) is the one that, as already mentioned, allows for a remarkable representation in terms of solids, as discussed in app. A. The violation of the Bell-Wigner inequality (5) due to quantum non-locality sho… view at source ↗
Figure 4
Figure 4. Figure 4: Qibo simulation for the Bell-Wigner inequality (5). The [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: QB QM is shown as a function of θac = θ. Left: for selected values of ϕ and taking θab = π/2. Right: for selected values of θab and taking ϕ = 0. It has to be stressed that the Bell inequality assumes perfect anti-correlation, as discussed in app. C: if one particle is measured along a given axis with spin-up, the other must be spin￾down. This is crucial because local hidden variable theories predict deter… view at source ↗
Figure 6
Figure 6. Figure 6: Qibo simulation for the Bell 1964 inequality (12). The [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: QS QM, that is the left-hand side of CHSH inequality (20) according to quantum mechanics, is shown as a function of θac. Left: taking ϕ = 0 and selected values of θab = θcd. Right: taking θab = θcd = π/2 and selected values of ϕ. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Qibo simulation of the CHSH inequality. The [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Polar plot of the Qibo simulation for the CHSH inequality, for selected values of [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Some of the possible sources of noise of a quantum device. [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visualization of the pair of particles belonging to population 3, flying apart and being measured by A and B, along one of the coplanar directions aˆ, ˆb and cˆ, with the predetermined result written on the faces orthogonal to the corresponding direction. This visually helps to show how the LH variables have been introduced. The initial particles are assumed not to be all equal to each other when entangle… view at source ↗
read the original abstract

We present educational material about Bell inequalities in the context of quantum computing. In particular, we provide software tools to simulate their violation, together with a guide for the classroom discussion. The material is organized in three modules of increasing difficulty, and the relative implementation has been written in Qibo, an open-source software suite to simulate quantum circuits with the ability to interface with quantum hardware. The topic of inequalities allows not only to introduce undergraduate or graduate students to crucial theoretical issues in quantum mechanics -- like entanglement, correlations, hidden variables, non-locality --, but also to practically put hands on tools to implement a real simulation, where statistical aspects and noise coming from current quantum chips also come into play.

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 presents educational material on Bell inequalities in quantum mechanics, using the open-source Qibo framework to provide simulation tools for their violation. The content is structured into three modules of increasing difficulty, accompanied by a classroom discussion guide; the goal is to introduce undergraduate and graduate students to concepts such as entanglement, hidden variables, correlations, and non-locality while incorporating statistical effects and hardware noise.

Significance. If the supplied Qibo implementations are correct and the modules are classroom-tested, the work supplies a concrete, open-source pedagogical resource that combines theoretical exposition with executable quantum-circuit simulations. This directly addresses the scarcity of accessible, hardware-aware teaching materials on Bell tests and can be adopted or adapted by instructors without requiring them to develop code from scratch.

minor comments (3)
  1. [Abstract / §1] The abstract and introduction refer to 'three modules of increasing difficulty' without listing their titles or one-sentence objectives; adding this information (perhaps as a short enumerated list in §1) would allow readers to gauge scope immediately.
  2. The manuscript states that implementations 'have been written in Qibo' but does not indicate whether the source code is included as supplementary material, deposited in a public repository, or only described at a high level; an explicit statement with a DOI or URL is needed for reproducibility.
  3. Figure captions and any circuit diagrams should explicitly state the Qibo version, backend (e.g., qibojit or qibolab), and whether the plotted statistics include simulated noise or ideal counts, to avoid ambiguity when readers attempt to reproduce the results.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and the recommendation for minor revision. The report correctly identifies the educational value of the three modules and the classroom discussion guide as an open-source resource for teaching Bell inequalities, entanglement, and related concepts with Qibo simulations that incorporate statistical and noise effects.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents educational software tools and classroom modules for simulating Bell inequality violations in Qibo. It contains no derivations, equations, predictions, or fitted parameters that could reduce to inputs by construction. The central claim is the provision of descriptive pedagogical material, which is self-contained and externally verifiable without reference to any internal chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities because the paper introduces no new scientific claims or derivations.

pith-pipeline@v0.9.0 · 5642 in / 795 out tokens · 38028 ms · 2026-05-23T07:21:21.294623+00:00 · methodology

discussion (0)

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Reference graph

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