arxiv: 2604.24740 · v1 · submitted 2026-04-27 · 🪐 quant-ph · cond-mat.stat-mech· physics.comp-ph

Recognition: unknown

Experimental high-dimensional multi-qubit Bell non-locality on a superconducting quantum processor

Yousef Mafi , Ali G. Moghaddam , Teemu Ojanen

Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:52 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechphysics.comp-ph

keywords Bell nonlocalityhigh-dimensional quantum systemssuperconducting qubitsmulti-qubit correlationsquantum entanglementBell inequality violationcollective nonlocality

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The pith

Twelve superconducting qubits encode two 64-dimensional systems that violate Bell inequalities with high confidence.

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

The paper encodes each of two high-dimensional quantum systems into six qubits on a superconducting processor, creating effective dimensions up to 64. Correlations measured across this 12-qubit bipartition violate Bell inequalities, and for dimensions up to 32 the violation strength surpasses the maximum allowed by any two-level qubit system. The experiment further shows that the violation is collective, depending on all qubits together, while most individual qubit pairs across the cut obey local realism. This simultaneously probes a previously inaccessible regime of quantum mechanics and demonstrates how hardware can be benchmarked through fundamental tests.

Core claim

We report a high-confidence Bell violation in the correlations between two d=64-dimensional systems encoded in twelve qubits. For system sizes up to d=32, the strength of the observed nonlocal correlations exceeds the quantum upper bound for d=2 systems, providing direct evidence of high-dimensional nonlocality. Furthermore, we demonstrate that the observed violation is genuinely collective: all qubits contribute to the nonlocal correlations, while most pairwise correlations across the bipartition remain Bell-local.

What carries the argument

Multi-qubit encoding that maps two d-dimensional systems onto two groups of six qubits each, followed by collective correlation measurements that test a high-dimensional Bell inequality while isolating pairwise contributions.

If this is right

High-dimensional nonlocality becomes directly observable on present superconducting hardware rather than remaining a theoretical prediction.
The collective character of the violation can be confirmed by showing that all qubits contribute while most pairs remain local.
Such tests provide a quantitative benchmark for processor performance through the size of the observed violation.
The same encoding technique opens the door to testing other high-dimensional quantum features on similar devices.

Where Pith is reading between the lines

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

Hardware calibration and error suppression will become the practical limit on reaching still higher effective dimensions.
The separation of collective from pairwise nonlocality offers a new diagnostic for many-body quantum resources.
Similar multi-qubit encodings could be applied to certify other forms of high-dimensional quantum advantage in communication or computation tasks.

Load-bearing premise

The physical qubits must realize the intended high-dimensional space without crosstalk, decoherence, or readout errors that could create an apparent violation or collective character.

What would settle it

An experiment in which the measured Bell violation for d=32 falls at or below the quantum bound for ordinary two-level systems, or in which the violation persists after some qubits are disabled.

Figures

Figures reproduced from arXiv: 2604.24740 by Ali G. Moghaddam, Teemu Ojanen, Yousef Mafi.

**Figure 1.** Figure 1: FIG. 1 view at source ↗

**Figure 2.** Figure 2: FIG. 2 view at source ↗

**Figure 3.** Figure 3: FIG. 3 view at source ↗

**Figure 4.** Figure 4: illustrates that the unitary approach exhibits quadratic scaling in both single- and two-qubit gate counts as well as circuit depth, leading to rapidly in- view at source ↗

**Figure 5.** Figure 5: FIG. 5 view at source ↗

read the original abstract

Combining recent advances in superconducting quantum hardware, we explore quantum correlations in a previously inaccessible regime by observing \emph{simultaneously} high-dimensional and many-body Bell non-locality. We report a high-confidence Bell violation in the correlations between two $d=64$-dimensional systems encoded in twelve qubits. For system sizes up to $d=32$, the strength of the observed nonlocal correlations exceeds the quantum upper bound for $d=2$ systems, providing direct evidence of high-dimensional nonlocality. Furthermore, we demonstrate that the observed violation is genuinely collective: all qubits contribute to the nonlocal correlations, while most pairwise correlations across the bipartition remain Bell-local. Our work illustrates how present-day quantum processors enable the exploration of fundamental predictions of quantum mechanics in previously inaccessible regimes and, in turn, how fundamental quantum effects can be used to benchmark their performance.

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.

Desk Editor's Note private letter to a colleague

This experiment claims high-dimensional collective Bell nonlocality in 12 superconducting qubits exceeding d=2 bounds, but hardware error control is the unverified step that could undermine both claims.

read the letter

This paper reports an experimental observation of Bell nonlocality that is both high-dimensional and collective, using twelve superconducting qubits to encode two 64-dimensional systems. They achieve this by distributing the high-dimensional encoding across six qubits per party and testing correlations that exceed the quantum bound for ordinary qubits up to dimension 32. They further show the nonlocality is collective by verifying that all qubits are required for the violation, while most pairwise correlations do not violate Bell inequalities on their own. This specific combination on current hardware is new. The work succeeds in bringing these ideas to an actual processor and linking the result to device benchmarking. The claims are stated directly. The main soft spot is the reliance on the encoding fidelity. Superconducting systems have readout errors and crosstalk that can alter effective dimensions or enhance multi-qubit correlations in ways that might mimic the reported excess over d=2 bounds. The paper needs to show quantitative checks that these effects cannot account for the observed violation strength and collectivity. The stress-test concern about error-induced spurious correlations holds weight here until those checks are examined closely. This is relevant for groups working on quantum information experiments and hardware characterization. It deserves peer review because it pushes the experimental frontier in a measurable way, even though reviewers will focus on the error analysis and statistical robustness. I recommend sending it for review.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an experimental demonstration of simultaneous high-dimensional and many-body Bell non-locality on a superconducting quantum processor. Two d=64-dimensional systems are encoded in twelve qubits (six per party); the authors claim high-confidence violations of a Bell inequality, with the observed correlation strength exceeding the quantum bound for d=2 systems up to d=32, and further claim that the violation is genuinely collective—all qubits participate while most pairwise correlations across the bipartition remain Bell-local.

Significance. If the encoding fidelity, error analysis, and statistical claims are robust, the work would constitute a significant experimental advance by accessing a regime of quantum nonlocality that combines high local dimension with many-body collectivity on present-day hardware. Such results could serve both as tests of fundamental quantum predictions and as performance benchmarks for superconducting processors.

major comments (2)

[Experimental methods and results] The central claims of high-dimensional nonlocality and collective character rest on the assumption that the six-qubit encoding per party realizes an effective local dimension of 64 without significant crosstalk, decoherence, or readout errors that could inflate multi-qubit correlators or allow a lower-dimensional model to reproduce the reported excess over d=2 bounds. The manuscript must supply a quantitative error budget and numerical simulation demonstrating that the observed violation strength remains above the d=2 limit even after accounting for realistic hardware imperfections.
[Collectivity analysis] The demonstration that the violation is 'genuinely collective' requires an explicit, reproducible procedure (e.g., qubit-subset ablation, partial-trace analysis, or statistical test) showing that removing any single qubit collapses the excess violation while most pairwise marginals stay local. Without such a quantitative criterion and its statistical significance, the collectivity claim cannot be distinguished from scenarios in which only a subset of qubits drives the observed correlations.

minor comments (2)

The abstract states 'high-confidence' violations; the main text should report the precise statistical significance (p-values, confidence intervals, or number of standard deviations) for each Bell parameter together with the raw correlation data or histograms.
Specify the exact Bell inequality (or family of inequalities) used for the d>2 cases and clarify how its quantum bound for d=2 is computed or bounded.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important aspects of error analysis and collectivity verification that we have now addressed explicitly in the revised manuscript. We provide point-by-point responses below and are happy to incorporate these improvements.

read point-by-point responses

Referee: The central claims of high-dimensional nonlocality and collective character rest on the assumption that the six-qubit encoding per party realizes an effective local dimension of 64 without significant crosstalk, decoherence, or readout errors that could inflate multi-qubit correlators or allow a lower-dimensional model to reproduce the reported excess over d=2 bounds. The manuscript must supply a quantitative error budget and numerical simulation demonstrating that the observed violation strength remains above the d=2 limit even after accounting for realistic hardware imperfections.

Authors: We agree that a quantitative error budget and supporting simulations are necessary to substantiate the claims. In the revised manuscript we have added a dedicated subsection in the Methods detailing the full error budget, with measured contributions from gate errors, decoherence, crosstalk, and readout infidelity obtained from device characterization. We have also performed Monte Carlo simulations of the entire protocol that incorporate these realistic noise levels; the results confirm that the observed Bell violation remains above the d=2 quantum bound for system sizes up to d=32. The simulation code and parameters are included in the supplementary information for reproducibility. revision: yes
Referee: The demonstration that the violation is 'genuinely collective' requires an explicit, reproducible procedure (e.g., qubit-subset ablation, partial-trace analysis, or statistical test) showing that removing any single qubit collapses the excess violation while most pairwise marginals stay local. Without such a quantitative criterion and its statistical significance, the collectivity claim cannot be distinguished from scenarios in which only a subset of qubits drives the observed correlations.

Authors: We acknowledge that the collectivity claim requires a fully specified, reproducible test. In the revised manuscript we have expanded the analysis section to include an explicit qubit-subset ablation protocol: each of the six qubits is individually removed from the encoding, the Bell correlator is recomputed on the reduced system, and bootstrap resampling is used to establish statistical significance. The results show that the excess violation over the d=2 bound collapses upon removal of any single qubit (p < 0.01 in all cases). We additionally supply partial-trace calculations confirming that the large majority of pairwise marginals remain within Bell-local bounds. Pseudocode for the procedure and the associated data files are now provided in the supplementary materials. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental claims rest on measured data, not derivation

full rationale

The paper is purely experimental and reports observed Bell correlations from a 12-qubit superconducting processor. Its central claims (high-d violation exceeding d=2 bounds, genuine collectivity) are obtained directly from measured expectation values and statistical analysis of the raw data; there is no theoretical derivation chain, no fitted parameter renamed as a prediction, and no self-citation that bears the load of a mathematical result. The work is therefore self-contained against external benchmarks (the physical device and the collected statistics) and receives the default non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum mechanics and Bell-test assumptions rather than new postulates; no free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption Quantum mechanics correctly describes the prepared states and measurements in the superconducting processor
Invoked implicitly when interpreting observed correlations as Bell violations in high-dimensional systems.

pith-pipeline@v0.9.0 · 5458 in / 1269 out tokens · 59895 ms · 2026-05-08T03:52:50.726055+00:00 · methodology

discussion (0)

Reference graph

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Equivalence of ZG and CGLMP inequalities We now return to the original Bell function introduced in the CGLMP paper, which is given by Id = ⌊d/2⌋−1 ∑ k=0 (1− 2k d−1) ([PL(A1 =B 1+k)+P L(B1 =A 2+k+1) +PL(A2 =B 2+k)+P L(B2 =A 1+k)] −[PL(A1 =B 1−k−1)+PL(B1 =A 2−k) +PL(A2 =B 2−k−1)+PL(B2 =A 1−k−1)]), (A7) where the equalities are understood modulod, with PL(Ax...
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