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arXiv:2406.07659 · Physical Review A

Generating multipartite nonlocality to benchmark quantum computers

Jan Lennart Bönsel, Otfried Gühne, Adán Cabello

Published Jan 9, 2025• 7 citations
arXivHTMLPDF

Abstract

We show that quantum computers can be used for producing large $n$-partite nonlocality, thereby providing a method to benchmark them. The main challenges to overcome are as follows: (i) The interaction topology might not allow arbitrary two-qubit gates. (ii) Noise limits the Bell violation. (iii) The number of combinations of local measurements grows exponentially with $n$. To overcome (i), we point out that graph states that are compatible with the two-qubit connectivity of the computer can be efficiently prepared. To mitigate (ii), we note that for specific graph states, there are $n$-partite Bell inequalities whose resistance to white noise increases exponentially with $n$. To address (iii) for any $n$ and any connectivity, we introduce an estimator that relies on random sampling. As a result, we propose a method for producing $n$-partite Bell nonlocality with unprecedented large $n$. This allows one, in return, to benchmark nonclassical correlations regardless of the number of qubits or the connectivity. We test our approach by using a simulation for a noisy IBM quantum computer, which predicts $n$-partite Bell nonlocality for at least $n=24$ qubits.

DOI
10.1103/physreva.111.012207

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We show that quantum computers can be used for producing large nnn-partite nonlocality, thereby providing a method to benchmark them. The main challenges to overcome are as follows: (i) The interaction topology might not allow arbitrary two-qubit gates. (ii) Noise limits the Bell violation. (iii) The number of combinations of local measurements grows exponentially with nnn. To overcome (i), we point out that graph states that are compatible with the two-qubit connectivity of the computer can be efficiently prepared. To mitigate (ii), we note that for specific graph states, there are nnn-partite Bell inequalities whose resistance to white noise increases exponentially with nnn. To address (iii) for any nnn and any connectivity, we introduce an estimator that relies on random sampling. As a result, we propose a method for producing nnn-partite Bell nonlocality with unprecedented large nnn. This allows one, in return, to benchmark nonclassical correlations regardless of the number of qubits or the connectivity. We test our approach by using a simulation for a noisy IBM quantum computer, which predicts nnn-partite Bell nonlocality for at least n=24n=24n=24 qubits.
In this work, we study a recently proposed operational measure of nonlocality by Fonseca and Parisio~[Phys. Rev. A 92, 030101(R) (2015)] which describes the probability of violation of local realism under randomly sampled observables, and the strength of such violation as described by resistance to white noise admixture. While our knowledge concerning these quantities is well established from a theoretical point of view, the experimental counterpart is a considerably harder task and very little has been done in this field. It is caused by the lack of complete knowledge about the facets of the local polytope required for the analysis. In this paper, we propose a simple procedure towards experimentally determining both quantities for NNN-qubit pure states, based on the incomplete set of tight Bell inequalities. We show that the imprecision arising from this approach is of similar magnitude as the potential measurement errors. We also show that even with both a randomly chosen NNN-qubit pure state and randomly chosen measurement bases, a violation of local realism can be detected experimentally almost 100%100\%100% of the time. Among other applications, our work provides a feasible alternative for the witnessing of genuine multipartite entanglement without aligned reference frames.
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Abstract We propose an optimal and efficient numerical test for witnessing genuine multipartite nonlocality based on a geometric approach. In particular, we consider two non-equivalent models of local hidden variables, namely the Svetlichny and the no-signaling bilocal models. While our knowledge concerning these models is well established for Bell-type scenarios involving two measurement settings per party, the general case based on an arbitrary number of settings is a considerably more challenging task and very little work has been done in this field. In this paper, we applied such general tests to detect and characterize genuine n-way nonlocal correlations for various states of three qubits and qutrits. Apart from the fundamental problem of characterizing genuine multipartite nonlocal correlations, the extension of the number of measurements beyond two is also of practical importance. As a measure of nonlocality, we use the probability of violation of local realism under randomly sampled observables, and the strength of nonlocality, described by the resistance to white noise admixture. In particular, we analyze to what extent the Bell-type scenario involving two measurement settings can be used to certify genuine n-way nonlocal correlations generated for more general models. In addition, we propose a simple procedure to detect such nonlocal correlations for randomly chosen settings with an efficiency of up to 100%. Due to its near-perfect efficiency, our method may open new possibilities in device-independent quantum cryptography applications where strong nonlocality between all partners is required.
Abstract Bell nonlocality—the existence of quantum correlations that cannot be explained by classical means—is certainly one of the most striking features of quantum mechanics. Its range of applications in device-independent protocols is constantly growing. Many relevant quantum features can be inferred from violations of Bell inequalities, including entanglement detection and quantification, and state certification applicable to systems of arbitrary number of particles. A complete characterisation of nonlocal correlations for many-body systems is, however, a computationally intractable problem. Even if one restricts the analysis to specific classes of states, no general method to tailor Bell inequalities to be violated by a given state is known. In this work we provide a general construction of Bell expressions tailored to the graph states of any prime local dimension. These form a broad class of multipartite quantum states that have many applications in quantum information, including quantum error correction. We analytically determine their maximal quantum values, a number of high relevance for device-independent applications of Bell inequalities. Importantly, the number of expectation values to determine in order to test the violation of our inequalities scales only linearly with the system size, which we expect to be the optimal scaling one can hope for in this case. Finally, we show that these inequalities can be used for self-testing of multi-qutrit graph states such as the well-known four-qutrit absolutely maximally entangled state AME(4,3).
Multipartite Bell tests provide a correlation-only route to benchmarking quantum processors, but their application at large scales is hindered by the rapid decay of many-body correlators under noise and exponentially many terms in conventional Bell expressions. Here we address these scalability obstacles by introducing a finite-setting generalized Mermin family of state-tailored Bell inequalities with analytic certification bounds, in which the measurement-setting number mmm provides an additional certification dimension complementary to the system size nnn. We show that, for the powers-of-two setting choices considered here, increasing mmm leaves the ideal normalized multipartite quantum value unchanged while lowering the relevant classical bounds, thereby strengthening the Bell-violation ratios and yielding an improved noise-robustness scaling compared to the standard Mermin inequality. We test this construction experimentally on a programmable superconducting processor by preparing Greenberger-Horne-Zeilinger (GHZ) states of up to 80 qubits. Using randomized sampling for direct Bell-operator estimation, we observe Bell ratios that grow exponentially with system size, certify a nonlocality depth of 14, and show that increasing mmm strengthens both the Bell ratio and depth certification. All results are obtained solely from measured correlators and analytical bounds, without readout correction, tomography, or model-based mitigation. Generalized Mermin inequalities therefore provide a sharper Bell benchmark for noisy large-scale GHZ states.
Multipartite Bell nonlocality provides a device-independent probe of many-body quantum correlations, but its characterization is limited by the rapid growth of the underlying classical and quantum optimization problems. We develop a scalable method for constructing and certifying permutationally invariant Bell inequalities using only one- and two-body correlators. The construction gives families of inequalities with robust quantum violations for general mmm measurements as the number of parties NNN becomes large. To improve robustness against noise, we optimize the ratio of the quantum value to the classical bound for these families in the large-NNN limit. We then certify the resulting quantum violation using semidefinite programming. For the broad class of Bell inequalities studied here, the infinite-NNN ratios take simple rational values for finite mmm and converge to coth⁡(1)\coth(1)coth(1) as m→∞m\to\inftym→∞. The optimized inequalities efficiently detect many-body Bell nonlocality with collective measurements, with more measurement settings leading to stronger violations.