The work in this thesis focuses on the subject of quantum nonlocality. The fact that the principle of locality is violated in nature is among the most counter-intuitive revelations of the past century. The original proof of the nonlocal nature of quantum mechanics relies on the so-called measurement independence assumption. This assumption has come under scrutiny in recent years, mostly because nonlocality and its implications have found their way into the realm of potential applications. In this thesis, the measurement independence assumption is relaxed and replaced by a form of limited measurement dependence. The resulting set is analyzed and it is shown that the nonlocal features of quantum mechanics resist arbitrary lack of free choice. Additionally, a new perspective on how to deal with the so-called detection loophole is provided by the definition of limited detection locality. Finally, work on applications of quantum nonlocality, specifically entanglement certification and quantification is presented.
The work in this thesis focuses on the subject of quantum nonlocality. The fact that the principle of locality is violated in nature is among the most counter-intuitive revelations of the past century. The original proof of the nonlocal nature of quantum mechanics relies on the so-called measurement independence assumption. This assumption has come under scrutiny in recent years, mostly because nonlocality and its implications have found their way into the realm of potential applications. In this thesis, the measurement independence assumption is relaxed and replaced by a form of limited measurement dependence. The resulting set is analyzed and it is shown that the nonlocal features of quantum mechanics resist arbitrary lack of free choice. Additionally, a new perspective on how to deal with the so-called detection loophole is provided by the definition of limited detection locality. Finally, work on applications of quantum nonlocality, specifically entanglement certification and quantification is presented.
Despite the success of quantum mechanics in predicting the outcomes of experiments in many branches of physics, the foundations of the theory have remained subject of research and dispute. At the basis of this struggle with the theory lie the phenomena of nonlocality and entanglement. Since it was first predicted by Bell in 1964, nonlocality was not only verified in numerous experiments, but also identified as a useful resource for quantum information processing. Thus, the study of nonlocality is important both from a fundamental point of view and with respect to new applications in quantum information theory, such as secure cryptography and randomness generation. The identification of entanglement as a resource for quantum information led to a strong theoretical effort devoted to its characterisation and detection. Many of the resulting mathematical tools find application in several domains of physics. Although the only known way to create nonlocal correlations is to measure entangled quantum systems, it has been shown that entanglement and nonlocality constitute two inequivalent properties. Therefore, in the light of the success of entanglement theory, it is of interest to also devise a resource theory of nonlocality. The task of this thesis is to develop such a theoretical framework for the characterisation of nonlocality as a resource. To gain a better understanding of nonlocal correlations it will be necessary to investigate correlation scenarios that go beyond the situation originally considered by Bell. In doing so, this thesis provides new description of nonlocality that also have implications for the characterisation of quantum correlations and the detection of new forms of nonlocality. The first question we address is how nonlocality can consistently be defined in a scenario of arbitrarily many parties that may collaborate among each other. To this end we recognise which are the allowed physical operations in this situation and then define nonlocality as the resource that cannot be created by these operations. Our approach shows that the conventional definition of multipartite nonlocality, adopted by the community so far, is inconsistent with this operational definition; we further propose and analyse new models that do not suffer from these inconsistencies. Furthermore, we show that our findings have implications for the characterisation of quantum correlations. A recent approach to describe the set of quantum correlation consists in using principles inspired from information theory. By using a special instance of the models we defined earlier we show a fundamental limitation of this approach: no bipartite information principle is sufficient to single out the set of quantum correlations from the set of nonsignalling correlations. We then developed a description of nonlocality in an even more generalised scenario of several parties. Motivated by a result of Popescu we study scenarios where the parties are allowed to perform not only a single but sequences of measurements on their systems. Characterising nonlocality also in this scenario in operational terms and defining local models compatible with this definition, we show that a new form of nonlocality can be detected Lastly, we examine the problem of detecting the presence of nonlocality in a multipartite scenario when one is given only partial access to the global system. We find that one can verify that the total system must display nonlocality, even though the accessible subsystems only exhibit local correlations.
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.
Abstract In recent years, quantum nonlocality sharing has attracted widespread research attention. Nevertheless, all existing investigations are built upon the measurement independence assumption. The freedom‑of‑choice loophole originates when measurement settings and hidden variables cannot be guaranteed independent, which corresponds to the regime where the measurement independence assumption no longer holds. This paper pioneers the exploration of quantum nonlocality sharing under measurement-dependent scenarios. By integrating the inherent characteristics of measurement dependence with the optimization of measurement strategies for nonlocality sharing, and quantifying the performance of sequential-measurement-based nonlocality sharing via the experimental occurrence frequency of measurement dependence, we demonstrate that maintaining a certain degree of partial measurement independence is critical to achieving valid nonlocality sharing. Moreover, we analyze the correlation constraints imposed by measurement-dependent local models and clarify the physical boundary between correlations explainable by classical hidden-variable descriptions and those that cannot be reproduced by such models.
It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e., allowing for the source to be partially correlated with the choices of measurement settings; however, what is the minimal amount of measurement independence needed to observe quantum nonlocality? Here we explore this question and consider models with strong measurement-dependent locality, where measurement choices can be perfectly determined in almost all rounds of the Bell test. Nevertheless, we show that quantum nonlocality can still be observed in this scenario, which we conjecture is minimal within the framework we use. We also discuss potential applications in randomness amplification.
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.
The demonstration and use of nonlocality, as defined by Bell's theorem, rely strongly on dealing with nondetection events due to losses and detectors'inefficiencies. Otherwise, the so-called detection loophole could be exploited. The only way to avoid this is to have detection efficiencies that are above a certain threshold. We introduce the intermediate assumption of limited detection efficiency, that is, in each run of the experiment, the overall detection efficiency is lower bounded by η(min)>0. Hence, in an adversarial scenario, the adversaries have arbitrary large but not full control over the inefficiencies. We analyze the set of possible correlations that satisfy limited detection locality and show that they necessarily satisfy some linear Bell-like inequalities. We prove that quantum theory predicts the violation of one of these inequalities for all η(min)>0. Hence, nonlocality can be demonstrated with arbitrarily small limited detection efficiencies. We validate this assumption experimentally via a twin-photon implementation in which two users are provided with one photon each out of a partially entangled pair. We exploit on each side a passive switch followed by two measurement devices with fixed settings. Assuming the switches 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.