Experimental detection of multipartite Bell nonlocality faces many challenges. The increase in the size of the system demands a higher fidelity of state preparation, a higher detection efficiency, and a larger number of correlators that need to be estimated. These issues are even more pronounced if one wishes to detect a more restrictive variant of Bell nonlocality called genuine multipartite nonlocality (GMNL). In this work, we introduce two classes of multipartite Bell inequalities that are capable of detecting GMNL correlations and address different experimental hurdles in GMNL detection. The first class consists of the number of correlators that scales linearly with the number of parties. The second class increases the number of correlators and, in return, provides higher noise robustness of GMNL detection. Both classes of inequalities are constructed to detect GMNL in graph states, and in fact both can be used for self-testing of graph states and the performed measurements.
Experimental detection of multipartite Bell nonlocality faces many challenges. The increase in the size of the system demands a higher fidelity of state preparation, a higher detection efficiency, and a larger number of correlators that need to be estimated. These issues are even more pronounced if one wishes to detect a more restrictive variant of Bell nonlocality called genuine multipartite nonlocality (GMNL). In this work, we introduce two classes of multipartite Bell inequalities that are capable of detecting GMNL correlations and address different experimental hurdles in GMNL detection. The first class consists of the number of correlators that scales linearly with the number of parties. The second class increases the number of correlators and, in return, provides higher noise robustness of GMNL detection. Both classes of inequalities are constructed to detect GMNL in graph states, and in fact both can be used for self-testing of graph states and the performed measurements.
Abstract It remains an open question whether every pure multipartite state that is genuinely entangled is also genuinely nonlocal. Recently, a new general construction of Bell inequalities allowing the detection of genuine multipartite nonlocality (GMNL) in quantum states was proposed in Curchod et al (2019 New J. Phys. 21 023016) with the aim of addressing the above problem. Here we show how, in a simple manner, one can improve this construction to deliver finer Bell inequalities for detection of GMNL. Remarkably, we then prove one of the improved Bell inequalities to be powerful enough to detect GMNL in every three-qubit genuinely entangled state. We also generalize some of these inequalities to detect not only GMNL but also nonlocality depth in multipartite states and we present a possible way of generalizing them to the case of more outcomes.
Genuine multipartite Bell nonlocality (GMNL) aims at capturing correlations between many distant observers that are globally Bell nonlocal. A commonly used definition for GMNL is based on biseparable models constructed from non-signalling correlations. Here we uncover an effect of superactivation of GMNL in this framework. Specifically, by locally wiring together two copies of a biseparable correlation, i.e. not GMNL, one can obtain another correlation that is GMNL. We show that this is possible for any number of parties, and for quantum-realizable correlations. Finally, we show that superactivation of GMNL is also possible at the single-copy level, via a catalytic protocol involving only local wirings. These results question the operational meaning of this definition of GMNL.
Local measurements acting on entangled quantum states give rise to a rich correlation structure in the multipartite scenario. We introduce a versatile technique to build families of Bell inequalities witnessing different notions of multipartite nonlocality for any number of parties. The idea behind our method is simple: a known Bell inequality satisfying certain constraints, for example the Clauser–Horne–Shimony–Holt inequality, serves as the seed to build new families of inequalities for more parties. The constructed inequalities have a clear operational meaning, capturing an essential feature of multipartite correlations: their violation implies that numerous subgroups of parties violate the inequality chosen as seed. The more multipartite nonlocal the correlations, the more subgroups can violate the seed. We illustrate our construction using different seeds and designing Bell inequalities to detect k -way nonlocal multipartite correlations, in particular, genuine multipartite nonlocal correlations—the strongest notion of multipartite nonlocality. For one of our inequalities we prove analytically that a large class of pure states that are genuine multipartite entangled (GME) exhibit genuine multipartite nonlocality for any number of parties, even for some states that are almost product. We also provide numerical evidence that this family is violated by all GME pure states of three and four qubits. Our results make us conjecture that this family of Bell inequalities can be used to prove the equivalence between genuine multipartite pure-state entanglement and nonlocality for any number of parties.
Bell nonlocality provides the foundation for device-independent (DI) certification of quantum devices. We introduce a Bell inequality capable of identifying genuine multipartite nonlocality (GMNL) in an arbitrary m-partite scenario with an arbitrary odd number of measurements per party. Since the multi-setting nature of this inequality precludes the use of Jordan's Lemma, we construct an analytical sum-of-squares (SOS) decomposition to obtain the optimal quantum violation without assuming any bound on the Hilbert space dimension. This, in turn, enables self-testing of the shared entangled state and the corresponding measurement observables, up to local isometries, whose existence we confirm using a swap-based certification scheme. In addition, we show that our framework enables the extraction of maximal global DI randomness (m bits) at the optimal quantum violation, thereby exceeding previous limitations in the GMNL regime. Finally, we demonstrate that the architecture of our inequality yields improved robustness to noise as the number of measurement settings grows, ensuring experimental feasibility.
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 m measurements as the number of parties N 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-N limit. We then certify the resulting quantum violation using semidefinite programming. For the broad class of Bell inequalities studied here, the infinite-N ratios take simple rational values for finite m and converge to coth(1) as m→∞. The optimized inequalities efficiently detect many-body Bell nonlocality with collective measurements, with more measurement settings leading to stronger violations.
We address the question of assessing the number of particles sharing genuinely nonlocal correlations in a multipartite system. While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to many-body systems: Such inequalities usually rely on expectation values involving many parties, usually all, and require individual addressing of each party. In addition, known Bell inequalities for genuine nonlocality are composed of a number of expectation values that scales exponentially with the number of observers, which makes such inequalities impractical from the experimental point of view. In a recent work [Tura et al., Science 344, 1256 (2014)], it was shown that it is possible to detect nonlocality in multipartite systems using Bell inequalities with only two-body correlators. This opened the way for the detection of Bell correlations with trusted collective measurements through Bell correlation witnesses [Schmied et al., Science 352, 441 (2016)]. These witnesses were recently tested experimentally in many-body systems such as Bose-Einstein condensate or thermal ensembles, hence demonstrating the presence of Bell correlations with assumptions on the statistics. Here, we address the problem of detecting nonlocality depth, a notion that quantifies the number of particles sharing nonlocal correlation in a multipartite system. We introduce a general framework allowing us to derive Bell-like inequalities for nonlocality depth from symmetric two-body correlators. We characterize all such Bell-like inequalities for a finite number of parties and we show that they reveal Bell correlation depth $k\ensuremath{\le}6$ in arbitrarily large systems. We then show how Bell correlation depth can be estimated using quantities that are within reach in current experiments. On one hand, we use the standard multipartite Bell inequalities such the Mermin and Svetlichny ones to derive Bell correlations witnesses of any depth that involves only two collective measurements, one of which being the parity measurement. On the other hand, we show that our two-body Bell inequalities can be turned into witnesses of depth $k\ensuremath{\le}6$ that require measuring total spin components in certain directions. Interestingly, such a witness is violated by existing data from an ensemble of 480 atoms.