Bell's theorem establishes a fundamental incompatibility between quantum mechanics and local realism. However, persistent physical intuition suggests that local dynamical evolution or measurement-induced disturbances of local hidden variables might bypass this constraint. We establish a generalized transition-kernel framework encompassing dynamical measurement processes and rigorously prove that any dynamical model satisfying ontological parameter independence is mathematically reducible to a static Bell model. We reveal a fundamental trichotomy: to reproduce quantum correlations, a hidden-variable model must violate either (i) strict locality (e.g., ontological parameter and outcome independence), (ii) measurement independence, or (iii) realism. Our results provide a universal diagnostic tool, demonstrating that nonlocal statistical correlations can never be synthesized by purely local dynamical complexity.
Bell's theorem establishes a fundamental incompatibility between quantum mechanics and local realism. However, persistent physical intuition suggests that local dynamical evolution or measurement-induced disturbances of local hidden variables might bypass this constraint. We establish a generalized transition-kernel framework encompassing dynamical measurement processes and rigorously prove that any dynamical model satisfying ontological parameter independence is mathematically reducible to a static Bell model. We reveal a fundamental trichotomy: to reproduce quantum correlations, a hidden-variable model must violate either (i) strict locality (e.g., ontological parameter and outcome independence), (ii) measurement independence, or (iii) realism. Our results provide a universal diagnostic tool, demonstrating that nonlocal statistical correlations can never be synthesized by purely local dynamical complexity.
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.
In our contextual model, statistical independence is violated, thus it is not constrained by Bell Theorem. Individual outcomes are created locally in a deterministic way in a function of setting dependent variables describing measuring instruments and variables describing physical systems, at the moment of their interactions. These setting dependent variables may be correlated, but not necessarily due to spooky influences or superdeterminism. In several Bell Tests, two time series of distant clicks are converted into finite samples containing pairs of non zero outcomes. This data not only violates CHSH inequalities but also nonsignalling. Our model allows explaining both the raw and the final data in these experiments. Moreover, our model, does not compromise experimenters freedom of choice. The violation of nonsignaling is neither consistent with quantum description of an ideal EPRB experiment nor with standard local realistic and stochastic hidden variable models, thus the title of this article and its conclusion: Kupczynski escape route for local realism is not available are misleading.
Violations of Bell inequalities are commonly interpreted as evidence for either nonlocal dynamics or the failure of classical realism. In this work, we show that Bell-type correlations can arise without invoking superluminal influences, retrocausality, or local hidden variables, provided that the mapping between underlying configurations and observable outcomes is non-injective. We study a class of effective models in which multiple underlying states correspond to the same observable description. Such non-injective projections generically induce non-factorizable joint probability structures at the level of observables, even when the underlying description itself is fully local and deterministic. As a result, the statistical assumptions required to derive Bell inequalities are violated at the effective level, while locality is preserved at the underlying level. Within this framework, quantum correlations emerge as structural features of projected descriptions rather than as signatures of nonlocal causation. We clarify the precise assumption of Bell’s theorem that fails in this setting and show how classical behavior is recovered in regimes where the effective projection becomes approximately injective, suppressing nonlocal correlations through decoherence and environmental coarse-graining. Our results suggest that Bell inequality violations need not reflect a fundamental nonlocality of nature, but may instead indicate intrinsic information loss induced by non-injective mappings between underlying configurations and observable descriptions.
Quantum correlations that violate the Bell inequality cannot be explained by any local-hidden-variable theory that is measurement independent. However, this violation merely signifies the incompatibility of the underlying assumptions of reality, locality, and measurement independence, without providing a quantitative measure of the extent to which each assumption is violated. In contrast, Hall introduced a measure for each of the following assumptions: indeterminism, signaling, and measurement dependence, and Hall also generalized the Bell-Clauser-Horne-Shimony-Holt inequality, which provides a quantitative trade-off relationship between these assumptions. In this paper, we consider the introduction of hidden variables to be an essential assumption of Bell's theorem and introduce a quantification of hidden variables, which we term ``hiddenness.'' We derive a trade-off relation between hiddenness and measurement dependence that applies to any local-hidden-variable theory.
The standard interpretation of quantum measurement on entangled systems holds that measuring one particle nonlocally collapses the wavefunction of its spacelike-separated partner. We argue that this conclusion rests on a false presupposition: that subsystems of entangled systems possess independent ontic states. If the global wavefunction is the sole ontic object (ψ-ontic holism), then for entangled systems, there is no "state of B" to be affected by measurement at A. Measurement is a local dynamical process-concretely modeled by continuous spontaneous localization-that destroys one local wavefunction component at the measurement site; the global state factorizes as a consequence, and subsystem ontology emerges for the first time. The transition of the distant particle's reduced density matrix from mixed to pure reflects this emergence of separability, not a physical change at the distant location. The framework satisfies no-signaling and embraces the contextuality required by the Kochen-Specker and GHZ theorems. We are explicit about its relation to Bell's theorem: Bell local causality (factorizability) fails, as it must in any empirically adequate theory, but the failure is confined to outcome independence and is identified with the nonseparability of the global ontic state, while parameter independence-and with it the locality of the dynamics-holds exactly. Decoherence provides the mechanism by which the global wavefunction factorizes and classical separability emerges. The apparent nonlocality of quantum mechanics is thus reinterpreted as nonseparability: the fundamental ontology is holistic, but the dynamics are local.
In this Letter, we explore the possibility of developing Bell inequalities predicated on models using a single Local Hidden Variable (s-LHV), a strict subset of general LHV models. Because of the less strenuous constraints imposed by s-LHV models, we were able to derive a contingent Bell inequality in analogy to the CHSH inequality, but which does not require bounding of measurement statistics. Following this, we show by explicit example that there are cases of states that rule out s-LHV models by violating our inequality, but which nonetheless have a multivariate LHV model. Even so, we show how merely ruling out s-LHV models is still sufficient to allow for fully device independent quantum key distribution (QKD) and entanglement witnessing. This being the case, our inequality illustrates two things. First, it makes fully device-independent QKD on continuous variables substantially more straightforward. Second, it shows how the degree of correlation needed to demonstrate device-independent QKD is distinct from both Bell-nonlocality and EPR-steering. Although nonlocality in general requires ruling out all LHV models, s-LHV models are sufficiently useful to warrant further exploration.