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arXiv:2609.39411

Genuine Multipartite Nonlocality Is Fermionic Magic

Jamal Slim

quant-phSubmitted Sep 30, 2026• Announced Oct 1, 2026• 0 citations
v1 · Sep 30, 2026v2 · Oct 13, 2026
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Abstract

A system of free fermions can be simulated on a classical computer, and a single non-Gaussian state makes it a universal quantum computer. We show that the same line bounds quantum nonlocality. Measured as fermionic qubits, free fermions carry the Bell nonlocality of one entangled pair, no more, however many parties share them, and are never genuinely multipartite nonlocal. Fermion parity is the reason. Genuine multipartite nonlocality is thus the resource of universal fermionic computation, cannot arise from any mean-field state, and we certify it on $48$ qubits of IBM processors.

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A system of free fermions can be simulated on a classical computer, and a single non-Gaussian state makes it a universal quantum computer. We show that the same line bounds quantum nonlocality. Measured as fermionic qubits, free fermions carry the Bell nonlocality of one entangled pair, no more, however many parties share them, and are never genuinely multipartite nonlocal. Fermion parity is the reason. Genuine multipartite nonlocality is thus the resource of universal fermionic computation, cannot arise from any mean-field state, and we certify it on 484848 qubits of IBM processors.
Fermionic Gaussian states describe free fermions and underlie the mean-field picture of matter, from metals to superconductors; they are also efficiently simulable on classical computers. Departures from Gaussianity -- the correlations produced by interactions -- are therefore what make a fermionic system hard to simulate classically and useful for quantum computation, analogous to the role of magic in stabilizer-based quantum computation. Yet detecting and quantifying such non-Gaussianity at scale has remained challenging. Here we introduce practical tests and witnesses of fermionic non-Gaussianity built on fermionic antiflatness, a measure derived from the two-point covariance matrix. We estimate it with two protocols -- a two-copy Bell measurement and a single-copy scheme using commuting Majorana bilinears -- that determine whether a state is Gaussian or far from it at lower measurement cost than existing approaches, using only operations native to fault-tolerant hardware. For mixed states, a purity-corrected witness certifies non-Gaussianity and remains robust under strong noise; running it on the IQM quantum processor, we find that noise can both reduce and enhance non-Gaussianity. Finally, we show that preparing pseudorandom fermionic states requires extensive non-Gaussianity. Together, these tools enable the study and certification of non-Gaussian fermionic resources on present-day quantum devices.
Benchmarking quantum processors is a central task in every roadmap aimed at quantum advantage. Here, we discuss a benchmarking protocol based on the violation of the Svetlichny inequality, which is designed to simulate genuine multipartite nonlocality. We compare it with Mermin's inequality, and present the results of applying this framework to two different quantum processing units -the superconducting system Garnet (from IQM) and the ion-trap system Marmot (from AQT), testing different families of quantum circuits for three to five qubits under identical experimental conditions. We also run simultaneous triplet tests across the full register, including a comparison between GHZ and linear cluster states, to probe how Svetlichny-inequality violations depend on qubit location and calibration. Our results demonstrate that tests based on genuine multipartite nonlocality provide a powerful tool to characterize the collective performance of quantum devices and to guide their calibration and optimization.
We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.
The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions apprehend truly multipartite effects, given that these behaviours cannot be reproduced by bilocal models that allow correlations among strict subsets of the parties beyond a local common cause. We show here that, while in the so-called correlation scenario the relative violation of bilocal Bell inequalities by quantum resources is bounded, i.e. it does not grow arbitrarily with the number of inputs, it turns out to be unbounded in the general case. We identify Bell functionals that take the form of non-local games for which the ratio of the quantum and bilocal values grows unboundedly as a function of the number of inputs and outputs.
Quantum networks are built from independent sources, and their nonlocality has mostly been studied with sources that emit bipartite entangled states. A source of three entangled qubits is richer, since its nonlocality can be tested by the Mermin or the more demanding Svetlichny inequality. We ask how network nonlocality relates to these two single-source notions and find that the answer depends on the wiring. When two central nodes without inputs share every source, Bell-state measurements turn every Svetlichny violation into a network violation, and even all entangled generalised Greenberger-Horne-Zeilinger states violate the network inequality. When a single central node is shared, the relation reverses, and a network violation requires a Mermin violation of the source. With more sources, the maximal violation depends on whether their number is even or odd, and we give tight bounds for both cases. These results show that the way multipartite sources are wired decides which kind of nonlocality a network inherits.
Abstract The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions apprehend truly multipartite effects, given that these behaviours cannot be reproduced by bilocal models that allow correlations among strict subsets of the parties beyond a local common cause. We show here that, while in the so-called correlation scenario the relative violation of bilocal Bell inequalities by quantum resources is bounded, i.e. it does not grow arbitrarily with the number of inputs, it turns out to be unbounded in the general case. We identify Bell functionals that take the form of non-local games for which the ratio of the quantum and bilocal values grows unboundedly as a function of the number of inputs and outputs.