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arXiv:2407.19587 · Physical Review A

Strength of statistical evidence for genuine tripartite nonlocality

Soumyadip Patra, Peter Bierhorst

Published Dec 6, 2024• 1 citation
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Abstract

Recent advancements in network nonlocality have led to the concept of local operations and shared randomness-based genuine multipartite nonlocality (LOSR-GMNL). In this paper, we consider two recent experimental demonstrations of LOSR-GMNL, focusing on a tripartite scenario where the goal is to exhibit correlations impossible in a network where each two-party subset shares bipartite resources and every party has access to unlimited shared randomness. Traditional statistical analyses measuring violations of witnessing inequalities by the number of experimental standard deviations do not account for subtleties such as memory effects. We demonstrate a more sound method based on the prediction-based ratio protocol to analyze finite experimental data and quantify the strength of evidence in favor of genuine tripartite nonlocality in terms of a valid $p$ value. In our paper, we propose an efficient modification of the test factor optimization using an approximating polytope approach. By justifying a further restriction to a smaller polytope we enhance practical feasibility while maintaining statistical rigor.

DOI
10.1103/physreva.110.062411

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Recent advancements in network nonlocality have led to the concept of local operations and shared randomness-based genuine multipartite nonlocality (LOSR-GMNL). In this paper, we consider two recent experimental demonstrations of LOSR-GMNL, focusing on a tripartite scenario where the goal is to exhibit correlations impossible in a network where each two-party subset shares bipartite resources and every party has access to unlimited shared randomness. Traditional statistical analyses measuring violations of witnessing inequalities by the number of experimental standard deviations do not account for subtleties such as memory effects. We demonstrate a more sound method based on the prediction-based ratio protocol to analyze finite experimental data and quantify the strength of evidence in favor of genuine tripartite nonlocality in terms of a valid ppp value. In our paper, we propose an efficient modification of the test factor optimization using an approximating polytope approach. By justifying a further restriction to a smaller polytope we enhance practical feasibility while maintaining statistical rigor.
We study a strong form of genuine multipartite nonlocality (GMNL), where an nnn-partite scenario admits a quantum strategy generating outcomes belonging to a restricted set with certainty, whereas every strategy built from nonclassical resources shared among at most k<nk<nk<n parties fails this criterion with positive probability. This generalizes what is referred to as strong contextuality/nonlocality, or pseudotelepathy, beyond ruling out local models. For the simplest five-party Bell scenario of two binary-outcome measurement settings per party, we use the inflation technique to demonstrate that a game with a perfect quantum strategy witnesses a robust separation from models built from bipartite resources under local operations and shared randomness (LOSR), establishing the behavior is LOSR-GMNL. We provide broader context for this result by investigating its simulability with resources shared among three or four parties under different resource models and alternative definitions of GMNL. A central open question is whether nnn-party quantum resources can achieve such a separation from models built from (n−1)(n-1)(n−1)-party resources, for n≥3n\ge 3n≥3. We make progress here by constructing a family of robustly LOSR-GMNL games with εεε-optimal quantum strategies experimentally indistinguishable in the limit from true probability-one-winning strategies for any desired level of precision.
Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity (93.13±0.24)%, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.
Violation of the NNN-partite inequality introduced in Phys. Rev. Lett. 129, 150401 (2022) for genuine multipartite nonlocality under local operations and shared randomness (LOSR) rules out all causal-network models obtained by locally composing arbitrary resources involving at most N−1N-1N−1 parties, even when supplemented by shared randomness among all NNN parties. Here, we demonstrate a device-independent self-test protocol for this. We further establish an analytic noise-robust self-test. For a Bell-score deficit εεε, we derive explicit O(ε)O(\sqrtε)O(ε​) vector-norm bounds for the state and the corresponding measurement actions.
While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.
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.
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.