The Bell test, as an important method for detecting nonlocality, is widely used in device-independent quantum information processing tasks. The security of these tasks is based on an assumption called measurement independence. Since this assumption is difficult to be guaranteed in practical Bell tests, it is meaningful to consider the effect of reduced measurement independence (i.e., measurement dependence) on Bell tests. Some research studies have shown that nonlocality can be detected even if measurement dependence exists. However, the relevant results are all based on bipartite Bell tests, and the results for multipartite Bell tests are still missing. In this paper, we explore this problem in the tripartite Svetlichny test. By considering flexible lower and upper bounds on the degree of measurement dependence, we obtain the relation among measurement dependence, guessing probability, and the maximal value of Svetlichny inequality. Our results reveal the case in which genuine nonlocality is nonexistent; at this point, the outcomes of the Bell test cannot be applied in device-independent quantum information processing tasks.
The Bell test, as an important method for detecting nonlocality, is widely used in device-independent quantum information processing tasks. The security of these tasks is based on an assumption called measurement independence. Since this assumption is difficult to be guaranteed in practical Bell tests, it is meaningful to consider the effect of reduced measurement independence (i.e., measurement dependence) on Bell tests. Some research studies have shown that nonlocality can be detected even if measurement dependence exists. However, the relevant results are all based on bipartite Bell tests, and the results for multipartite Bell tests are still missing. In this paper, we explore this problem in the tripartite Svetlichny test. By considering flexible lower and upper bounds on the degree of measurement dependence, we obtain the relation among measurement dependence, guessing probability, and the maximal value of Svetlichny inequality. Our results reveal the case in which genuine nonlocality is nonexistent; at this point, the outcomes of the Bell test cannot be applied in device-independent quantum information processing tasks.
Bell tests, as primitive tools to detect nonlocality in bipartite systems, rely on an assumption, i.e., measurement independence. Since ensuring measurement independence in a practical Bell test is difficult, it is crucial to explore the effects of relaxing this assumption. Recently, in the simplest Clauser-Horne-Shimony-Holt Bell (CHSH-Bell) test, Koh et al. [Phys. Rev. Lett. 109, 160404 (2012)] built the relation among measurement dependence, guessing probability, and the maximum value of CHSH-Bell correlation function that an adversary (Eve) can fake. As well, Pope et al. [Phys. Rev. A 88, 032110 (2013)] and Yuan et al. [Phys. Rev. A. 91, 032111 (2015)] settled the same problem in the multiple-run scenario with the general input distribution and the factorizable one, respectively. However, pertinent results in the generalized CHSH-Bell test are still missing. Here, we study this problem and establish the relation among measurement dependence, guessing probability, and the maximum value of the generalized CHSH-Bell correlation function that Eve can fake. Furthermore, we also consider the multiple-run scenario and show the relations in both input distributions. Interestingly, compared with the simplest CHSH-Bell test, we find that it is more difficult for Eve to fake a violation in the generalized CHSH-Bell test in some special cases. We expect that our conclusions will serve as a reference for quantum information processing tasks such as quantum key distribution, randomness expansion, and other tasks in the device-independent framework.
Quantum nonlocality stands as a resource for device independent quantum information processing (DIQIP). It finds repercussions in applications such as, among others, quantum key distribution and generation of randomness. In this work, we investigate two different approaches to attest nonlocality. First we follow the assumption of limited measurement dependence, i.e., that the measurement settings used in Bell inequality tests or DIQIP are partially influenced by the source of entangled particles and/or by an adversary. Then, we introduce the intermediate assumption of limi- ted detection efficiency, that is, in each run of the experiment, the overall detection efficiency is lower bounded by eta_min > 0. Hence, in an adversarial scenario, the adversaries have arbitrary large but not full control over the inefficiencies. We analyse the set of possible correlations that fulfil Measurement Dependence/Limited Detection Locality (MDL/LDL) and show that they necessarily satisfy some linear Bell-like inequalities. In both scenarios, quantum theory predicts the violation of such inequalities for l > 0 in the first case, and eta_min > 0 in the other. We validate these assumptions experimentally via a twin-photon implementation in which two users are provided each with one photon out of a partially entangled pair. On one hand, we show with the first inequality that the measurement independence assumption can be widely relaxed while still demonstrating quantum nonlocality. On the other hand with the second inequality, assuming the switches between the measurement bases are not fully controlled by an adversary, nor by hypothetical local variables, we reveal the nonlocality of the established correlations despite a low overall detection efficiency.
In a multipartite setting, it is possible to distinguish quantum states that are genuinely n-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely n-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of n-way nonlocality, which we argue are better motivated both from the point of view of the study of nature, and from the point of view of quantum information theory. We show that these definitions are strictly weaker than Svetlichny's, and introduce a series of suitable Bell-type inequalities for the detection of three-way nonlocality. Numerical evidence suggests that all three-way entangled pure quantum states can produce three-way nonlocal correlations.
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.
The demonstration and use of Bell-nonlocality, a concept that is fundamentally striking and is at the core of applications in device independent quantum information processing, relies heavily on the assumption of measurement independence, also called the assumption of free choice. The latter cannot be verified or guaranteed. In this paper, we consider a relaxation of the measurement independence assumption. We briefly review the results of Phys. Rev. Lett. 113, 190402 (2014), which show that with our relaxation, the set of so-called measurement dependent local (MDL) correlations is a polytope, i.e. it can be fully described using a finite set of linear inequalities. Here we analyze this polytope, first in the simplest case of 2 parties with binary inputs and outputs, for which we give a full characterization. We show that partially entangled states are preferable to the maximally entangled state when dealing with measurement dependence in this scenario. We further present a method which transforms any Bell-inequality into an MDL inequality and give valid inequalities for the case of arbitrary number of parties as well as one for arbitrary number of inputs. We introduce the assumption of independent sources in the measurement dependence scenario and give a full analysis for the bipartite scenario with binary inputs and outputs. Finally, we establish a link between measurement dependence and another strong hindrance in certifying nonlocal correlations: nondetection events.
Quantum nonlocality stands as a resource for device independent quantum information processing (DIQIP), such as, for instance, device independent quantum key distribution. We investigate, experimentally, the assumption of limited measurement dependence, i.e., that the measurement settings used in Bell inequality tests or DIQIP are partially influenced by the source of entangled particle and/or by an adversary. Using a recently derived Bell-like inequality [G. Pütz, Phys. Rev. Lett. 113, 190402 (2014)] and a 99% fidelity source of partially entangled polarization photonic qubits, we obtain a clear violation of the inequality, excluding a much larger range of measurement dependent local models than would be possible with an adapted Clauser-Horne-Shimony-Holt (CHSH) inequality. It is therefore shown that the measurement independence assumption can be widely relaxed while still demonstrating quantum nonlocality.