Bell nonlocality, the fact that local hidden-variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental implications, nonlocality is also at the core of device-independent quantum information processing, the successful implementation of which is achieved without precise knowledge of the physical apparatus. Here we show that a stronger form of Bell nonlocality, for which even some nonlocal hidden-variable models cannot reproduce the quantum predictions, allows us to circumvent possible attacks in the implementation of secret sharing, a paradigmatic communication protocol in which a secret split amid many possibly untrusted parts can be decoded only if they collaborate among themselves.
Bell nonlocality, the fact that local hidden-variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental implications, nonlocality is also at the core of device-independent quantum information processing, the successful implementation of which is achieved without precise knowledge of the physical apparatus. Here we show that a stronger form of Bell nonlocality, for which even some nonlocal hidden-variable models cannot reproduce the quantum predictions, allows us to circumvent possible attacks in the implementation of secret sharing, a paradigmatic communication protocol in which a secret split amid many possibly untrusted parts can be decoded only if they collaborate among themselves.
Bell nonlocality is the experimentally testable incompatibility between quantum correlations and explanations based on local hidden variables. Its significance now extends beyond the foundations of quantum mechanics: a Bell-inequality violation can certify entanglement, randomness, measurement incompatibility, and cryptographic security without requiring a detailed model of the devices producing the observed data. This article develops the mathematical structure of Bell experiments and explains its role in device-independent quantum information. Conditional probability distributions are classified into local, quantum, and no-signalling sets; the Clauser-Horne-Shimony-Holt inequality is derived, and its classical, quantum, and algebraic limits are distinguished. Tsirelson’s bound is obtained from the CHSH operator, while Popescu-Rohrlich correlations demonstrate that no-signalling alone does not identify the quantum set. The relation between entanglement and nonlocality is examined through local entangled states, hidden nonlocality, and activation. Nonlocal games, semidefinite relaxations, self-testing, certified randomness, and device-independent quantum key distribution are treated as operational consequences of Bell violation. Particular attention is given to entropy accumulation, finite-data security, loophole-free experiments, and the limitations of device independence. Bell nonlocality emerges as both a foundational separation between classical and quantum causal models and a quantitative resource for cryptographic and informational tasks.
Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state: ρα=α|Φ+⟩⟨Φ+|+(1−α)14. We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for α>0.559 and α>12 , in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of 0.697 for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.
Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: first, a bipartite nonlocal quantum state is distributed between the honest users, who perform local projective measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by postprocessing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when implemented on any correlation obtained by measuring local projective measurements on certain entangled nonlocal states, namely, on a range of entangled two-qubit Werner states. To prove this result, we introduce a technique for upper bounding the asymptotic key rate of device-independent quantum key distribution protocols, based on a simple eavesdropping attack. Our results imply that either different reconciliation techniques are needed for device-independent quantum key distribution in the large-noise regime, or Bell nonlocality is not sufficient for this task.
The phenomenon of nonlocality, which can arise when entangled quantum systems are suitably measured, is perhaps one of the most puzzling features of quantum theory to the philosophical mind. It implies that these measurement statistics cannot be explained by hidden variables, as requested by Einstein, and it thus suggests that our universe may not be, in principle, a well-determined entity where the uncertainty we perceive in physical observations stems only from our lack of knowledge of the whole. Besides its philosophical impact, nonlocality is also a resource for information- theoretic tasks since it implies secrecy: If nonlocality limits the predictive power that any hidden variable (in the universe) can have about some observations, then it limits in particular the predictive power of a hidden variable held by an adversary in a cryptographic scenario. We investigate whether nonlocality alone can empower two parties to perform unconditionally secure communication in a feasible manner when only a provably minimal set of assumptions are made for such a task to be possible — independently of the validity of any physical theory (such as quantum theory). Nonlocality has also been of interest in the study of foundations of quantum theory and the principles that stand beyond its mathematical formalism. In an attempt to single out quantum theory within a broader set of theories, the study of nonlocality may help to point out intuitive principles that distinguish it from the rest. In theories where the limits by which quantum theory constrains the strength of nonlocality are surpassed, many “principles” on which an information theorist would rely on are shattered — one example is the hierarchy of communication complexity as the latter becomes completely trivial once a certain degree of nonlocality is overstepped. In order to study the structure of such super-quantum theories — beyond their aforementioned secrecy aspects — we investigate the phenomenon of distillation of nonlocality, the ability to distill stronger forms of nonlocality from weaker ones. By exploiting the inherent connection between nonlocality and secrecy, we provide a novel way of deriving bounds on nonlocality-distillation protocols through an ad versarial view to the problem.
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.
Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics. It is based on the assumption that Alice and Bob can choose measurements from a measurement set containing multiple elements. We establish a new paradigm that departs from Bell's paradigm by assuming that there are no choices for Alice and Bob and that the measurements Alice and Bob will make are fixed from the start. We include a process of quantum computation in our model. To the best of our knowledge, we are the first to connect quantum computation and nonlocality, the two faces of entanglement.