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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• Revised Oct 13, 2026 (v2)
v1 · Sep 30, 2026v2 · Oct 13, 2026
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Abstract

Free fermion dynamics is classically simulable, and a single non-Gaussian state makes it universal. We show that the same boundary governs quantum nonlocality. Measured as fermionic qubits, fermionic Gaussian states reach at most the biseparable bound of the Mermin inequality for three parties and, for any number of parties, violate the Mermin family by exactly the factor of a single entangled pair. They are never genuinely multipartite nonlocal. Genuine multipartite nonlocality and computational universality are thus one resource for fermions, the opposite of the stabilizer case. The mechanism is fermion parity. The bound is monogamous and certifies non-Gaussianity from measured correlations alone. On superconducting processors we watch nonlocality beyond free fermions switch on under an interaction between densities, confirm the monogamy law on 96 qubits, and measure the ground state of twelve interacting fermions on a ring cross the bound as the interaction grows, detecting the charge density wave transition.

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Free fermion dynamics is classically simulable, and a single non-Gaussian state makes it universal. We show that the same boundary governs quantum nonlocality. Measured as fermionic qubits, fermionic Gaussian states reach at most the biseparable bound of the Mermin inequality for three parties and, for any number of parties, violate the Mermin family by exactly the factor of a single entangled pair. They are never genuinely multipartite nonlocal. Genuine multipartite nonlocality and computational universality are thus one resource for fermions, the opposite of the stabilizer case. The mechanism is fermion parity. The bound is monogamous and certifies non-Gaussianity from measured correlations alone. On superconducting processors we watch nonlocality beyond free fermions switch on under an interaction between densities, confirm the monogamy law on 96 qubits, and measure the ground state of twelve interacting fermions on a ring cross the bound as the interaction grows, detecting the charge density wave transition.
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.
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.
Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of post-measurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in nnn-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems (i.e., the double-chain setting)[Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.