A stronger Bell argument for (some kind of) parameter dependence

Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities via the local probability model - the LqHV (local quasi hidden variable) model [Loubenets, J. Math. Phys. 53, 022201 (2012)], incorporating the LHV model only as a particular case and correctly reproducing the probabilistic description of every quantum correlation scenario, more generally, every nonsignaling scenario. The LqHV probability framework allows us to construct nonsignaling analogs of Bell inequalities and to specify parameters quantifying violation of Bell inequalities - Bell's nonlocality - in a general nonsignaling case. For quantum correlation scenarios on an N-qudit state, we evaluate these nonlocality parameters analytically in terms of dilation characteristics of an N-qudit state and also, numerically - in d and N. In view of our rigorous mathematical description of Bell's nonlocality in a general nonsignaling case via the local probability model, we argue that violation of Bell inequalities in a quantum case is not due to violation of the Einstein-Podolsky-Rosen (EPR) locality conjectured by Bell but due to the improper HV modelling of "quantum realism".

Quantum correlations which violate a Bell inequality are presumed to power better-than-classical protocols for solving communication complexity problems (CCPs). How general is this statement? We show that violations of correlation-type Bell inequalities allow advantages in CCPs, when communication protocols are tailored to emulate the Bell no-signaling constraint (by not communicating measurement settings). Abandonment of this restriction on classical models allows us to disprove the main result of, inter alia, \cite{BZ02}; we show that quantum correlations obtained from these communication strategies assisted by a small quantum violation of the CGLMP Bell inequalities do not imply advantages in any CCP in the input/output scenario considered in the reference. More generally, we show that there exists quantum correlations, with nontrivial local marginal probabilities, which violate the I3322 Bell inequality, but do not enable a quantum advantange in any CCP, regardless of the communication strategy employed in the quantum protocol, for a scenario with a fixed number of inputs and outputs

The violation of Bell, CHSH and CH inequalities indicates only that the assumption of "conterfactual definiteness" and/or the probabilistic models used in proofs were incorrect. In this paper we discuss in detail an intimate relation between experimental protocols and probabilistic models. In particular we show that local realistic and stochastic hidden variable models are inconsistent with the experimental protocols used in spin polarization correlation experiments. In particular these models neglect a contextual character of quantum theory (QT) and do not describe properly quantum measurements. We argue that the violation of various inequalities gives arguments against the irreducible randomness of act of the measurement. Therefore quantum probabilities are reducible what means that QT is emergent. In this case one could expect to discover in time series of data some unpredicted fine structures proving that QT is not predictably complete what would be a major discovery.

Correlations that violate a Bell inequality are said to be nonlocal; i.e., they do not admit a local and deterministic explanation. Great effort has been devoted to study how the amount of nonlocality (as measured by a Bell inequality violation) serves to quantify the amount of randomness present in observed correlations. In this work we reverse this research program and ask what do the randomness certification capabilities of a theory tell us about the nonlocality of that theory. We find that, contrary to initial intuition, maximal randomness certification cannot occur in maximally nonlocal theories. We go on and show that quantum theory, in contrast, permits certification of maximal randomness in all dichotomic scenarios. We hence pose the question of whether quantum theory is optimal for randomness; i.e., is it the most nonlocal theory that allows maximal randomness certification? We answer this question in the negative by identifying a larger-than-quantum set of correlations capable of this feat. Not only are these results relevant to understanding quantum mechanics' fundamental features, but also put fundamental restrictions on device-independent protocols based on the no-signaling principle.

Multipartite Nonlocality in Ontological Models of Quantum Theory

The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions apprehend truly multipartite effects, given that these behaviours cannot be reproduced by bilocal models that allow correlations among strict subsets of the parties beyond a local common cause. We show here that, while in the so-called correlation scenario the relative violation of bilocal Bell inequalities by quantum resources is bounded, i.e. it does not grow arbitrarily with the number of inputs, it turns out to be unbounded in the general case. We identify Bell functionals that take the form of non-local games for which the ratio of the quantum and bilocal values grows unboundedly as a function of the number of inputs and outputs.

A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. The latter has however some drawbacks. First and foremost it is unfeasible to determine the whole set of Bell inequalities already for a few measurements and thus unfeasible to find the experimental setup maximizing their violation. Second, the Bell violation suffers from an ambiguity stemming from the choice of the normalization of the Bell coefficients. An alternative measure of nonlocality with a direct information-theoretic interpretation is the minimal amount of classical communication required for simulating nonlocal correlations. In the case of many instances simulated in parallel, the minimal communication cost per instance is called nonlocal capacity, and its computation can be reduced to a convex-optimization problem. This quantity can be computed for a higher number of measurements and turns out to be useful for finding the optimal experimental setup. Focusing on the bipartite case, in this paper, we present a simple method for maximizing the nonlocal capacity over a given configuration space and, in particular, over a set of possible measurements, yielding the corresponding optimal setup. Furthermore, we show that there is a functional relationship between Bell violation and nonlocal capacity. The method is illustrated with numerical tests and compared with the maximization of the violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed by qutrits turns out to be even stronger if the nonlocal capacity is employed as a measure of nonlocality.

In this paper, we present an analog of Bell's inequalities violation test for N qubits to be performed in a nuclear magnetic resonance (NMR) quantum computer. This can be used to simulate or predict the results for different Bell's inequality tests, with distinct configurations and a larger number of qubits. To demonstrate our scheme, we implemented a simulation of the violation of the Clauser, Horne, Shimony and Holt (CHSH) inequality using a two-qubit NMR system and compared the results to those of a photon experiment. The experimental results are well described by the quantum mechanics theory and a local realistic hidden variables model (LRHVM) that was specifically developed for NMR. That is why we refer to this experiment as a simulation of Bell's inequality violation. Our result shows explicitly how the two theories can be compatible with each other due to the detection loophole. In the last part of this work, we discuss the possibility of testing some fundamental features of quantum mechanics using NMR with highly polarized spins, where a strong discrepancy between quantum mechanics and hidden variables models can be expected.

A fundamental particle in physical space subject to conservation of momentum and energy, and characterized by its average mass and its position is methodologically supplemented with an information processor – a classical Turing machine – and a randomizer both defined on an information space localized on every particle. In this way the particle can be considered a generalized Darwinian system on which natural selection could act steering the evolution on the information space of the algorithms that govern the behaviour of the particles, giving rise plausibly to emergent quantum behaviour from initial randomness. This theory is applied to an EPR-Bohm experiment for electrons in order to analyse Bell inequality violation. A model for the entanglement of two particles has been considered. The model includes shared randomness – each particle stores its own randomizer and that of its partner – and the mutual transfer of their algorithms – sharing programs – that contain their respective anticipation modules. This fact enables every particle to anticipate not only the possible future configurations of its surrounding systems, but also those of the surrounding systems of its entangled partner. Thus, while preserving locality and realism, this theory implies outcome dependence – through shared randomness – and parameter dependence – through shared anticipation – for entangled states and, as a consequence, the violation of the Bell inequality in an EPR-Bohm experiment.

Analytic formulas of Bell correlations are derived in terms of quantum probability statistics under the assumption of measuring outcome-independence and the Bell's inequalities (BIs) are extended to general bipartite-entanglement macroscopic quantum-states (MQS) of arbitrary spins. For a spin-½ entangled state we find analytically that the violations of BIs really resulted from the quantum nonlocal correlations. However, the BIs are always satisfied for the spin-1 entangled MQS. More generally the quantum nonlocality does not lead to the violation for the integer spins since the nonlocal interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spins due to the nontrivial Berry phase, and thus the violation of BIs is understood remarkably as an effect of geometric phase. Specifically, our generic observation of the spin-parity effect can be experimentally tested with the entangled photon-pairs.

Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the sole assumption of no signalling. We first investigate the trade-offs in Bell violations arising from the uncertainty relation for complementary binary observables, and exhibit several network configurations in which a tight trade-off arises in this fashion. We then derive a tight trade-off relation which cannot be obtained from the uncertainty relation showing that it does not capture monogamy entirely. The results are extended to Bell inequalities involving different number of parties and find applications in device-independent secret sharing and device-independent randomness extraction. Although two multipartite Bell inequalities may be violated simultaneously, we show that genuine multi-party non-locality, as evidenced by a generalised Svetlichny inequality, does exhibit monogamy property. Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations.

Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question, we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quantum, or even postquantum nature of a common cause. In particular, by considering the simplest instrumental scenario-for which violation of Bell inequalities is not possible-we show that every pure bipartite entangled state violates the classical bounds on causal influence, thus, answering in negative to the posed question and opening a new venue to explore the role of causality within quantum theory.

We consider quantum systems composed of $N$ qubits, and the family of all Bell's correlation inequalities for two two-valued measurements per site. We show that if a $N$-qubit state $\rho$ violates any of these inequalities, then it is at least bipartite distillable. Indeed there exists a link between the amount of Bell's inequality violation and the degree of distillability. Thus, we strengthen the interpretation of Bell's inequalities as detectors of useful entanglement.

Violations of Bell inequalities have been an incontestable indicator of non-classicality since the seminal paper by John Bell. However, recent claims of Bell inequalities violations with classical light have cast some doubts on their significance as hallmarks of non-classicality. Here, we challenge those claims. The crux of the problem is that such classical experiments simulate quantum probabilities with intensities of classical fields. However, fields intensities measurements are radically different from single-photon detections, which are primitives of any genuine Bell experiment. We show that this fundamental difference between field intensities measurements and single photon detections shifts the classical bound of relevant Bell inequalities to its non-signaling limit, leaving no place for their violations. Violations of Bell inequalities with classical light have profound implications but a new model leaves no space for such violations. Since the seminal paper by John Bell in 1964, which laid out a set of inequalities to test the theory of quantum mechanics, violations of the Bell inequalities have been used an indicator of non-classicality, or quantum-ness. However, recent claims of a violation of Bell inequalities with classical light have cast doubt on the suitability of using such tests as a hallmark of non-classicality. An international team of researchers from Poland and Singapore now present a model that shifts the classical bound of the Bell inequalities, limiting the space for violations with classical light.

Violation of local realism via Bell inequality—a profound and counterintuitive manifestation of quantum theory that conflicts with the prediction of local realism—is viewed to be intimately linked with quantum entanglement. Experimental demonstrations of such a phenomenon using quantum entangled states are among the landmark experiments of modern physics and paved the way for quantum technology. Here, we report the violation of the Bell inequality that cannot be described by quantum entanglement in the system but arises from quantum indistinguishability by path identity, shown by the multiphoton frustrated interference. By analyzing the measurement of four-photon frustrated interference within the standard Bell-test formalism, we find a violation of Bell inequality by more than four SDs. Our work establishes a connection between quantum correlation and quantum indistinguishability, providing insights into the fundamental origin of the counterintuitive characteristics observed in quantum physics.