Search Results (58)

Violations of Bell inequalities are commonly interpreted as evidence for nonlocal influences or as constraints on realist descriptions. We show that the failure of Bell-type factorizability arises naturally when observable outcomes are obtained through a non-injective mapping from an underlying configuration space. In this setting, the standard factorization assumption can be viewed as an implicit requirement that observable variables admit a jointly factorizable completion at the underlying level. We demonstrate that this requirement need not hold when the mapping from underlying configurations to observables is many-to-one. The resulting breakdown of probabilistic factorization does not rely on superluminal dynamics or hidden causal influences, but follows from information loss under projection. Observable outcomes correspond to equivalence classes of underlying configurations, preventing the assignment of independent local variables. We illustrate this mechanism with an explicit toy model producing Bell–CHSH violations while preserving operational no-signalling and statistical independence of measurement settings. The model is not intended to reproduce quantum correlations quantitatively, and may exceed the Tsirelson bound; its role is to isolate the structural origin of the violation. This analysis does not contradict Bell’s theorem, but identifies a class of effective descriptions for which its factorizability assumption does not apply. The framework preserves locality at the underlying level, introduces no additional hidden-variable dynamics, and does not modify quantum mechanics. It clarifies how classical factorization is recovered in regimes where the effective mapping becomes approximately injective. In the operator language of quantum theory, the same mechanism admits a natural reformulation in terms of reduction to an effective observable subalgebra by a noncommutative conditional expectation. Full article

In this paper we study photon entanglement in the framework of Maxwell–Schwartz field theory. The ambient state space is the complex Maxwellian distribution space $W={\mathcal{S}}^{\prime }({\mathbb{M}}_4,{\mathbb{C}}^3)$, whose elements are fields of the form $F=\overrightarrow{E}+ic\overrightarrow{B}$. Polarization is realized as a two-dimensional complex subspace of W, generated by suitable linearly polarized Maxwellian solutions associated with opposite propagation directions. This yields canonical polarization sectors $P_A$ and $P_B$, each naturally isomorphic to ${\mathbb{C}}^2$. Within this setting, the Bell singlet state is represented by a non-factorizable tensorial Maxwellian field in $P_A\otimes P_B\subset W\otimes W$. By means of the induced rotated polarization bases, the standard joint probabilities of the photon polarization experiment are recovered exactly, and the correlation law $E(a,b)=-cos\left(2\right(a-b\left)\right)$ is obtained. Consequently, the usual CHSH value $2\sqrt{2}$ is reproduced in the Maxwell–Schwartz framework. To clarify the meaning of this violation, we first formulate the CHSH inequality in a purely measure-theoretic form, as a theorem about four correlators represented on a single probability space by bounded measurable functions. We then show that the correlators produced by the intrinsic Maxwellian Bell state do not admit such a common representation. The obstruction is structural: the ontic state is a global non-product field configuration, and the four correlations arise from different polarization resolutions of the same tensorial Maxwellian state. A second main result concerns the Born rule. For $L^2$ scalar quantum states in the domain of the Maxwellian correspondence, we prove that the squared Hilbert norm, times the constant ${\epsilon }_0$, coincides with the electromagnetic energy of the associated field. This leads to an energy interpretation of the Born rule: the Born probability density is identified with the normalized electromagnetic energy density up to an interference term depending on the chosen Maxwell–Schwartz isomorphism, which assumes the role of a quantum context. In the context of the Aspect and collaborators’ experiment, we prove that, on the other hand, the polarization probabilities become energy contributions of the corresponding field components. These results show that photon entanglement, Bell inequality violation, and the Born rule admit a coherent interpretation within Maxwell–Schwartz field theory, where the basic ontological objects are electromagnetic-like fields rather than abstract state vectors. Full article

Bell–CHSH is an inequality about unconditional expectations: under measurement independence, Bell locality, and bounded outcomes, the CHSH value satisfies $S\le 2$. Experimental correlators, however, are often computed on an accepted subset of trials defined by detection logic, coincidence matching, quality cuts, and analysis windows. We model this by an acceptance probability $\gamma (a,b,\lambda )\in [0,1]$ and the resulting accepted hidden-variable law ${\nu }_{ab}$ obtained by weighting the measurement-independent prior $\rho$ by $\gamma$ and renormalizing. If ${\nu }_{ab}$ depends on the setting pair then the four correlators entering CHSH are expectations under four different measures, and a Bell-local measurement-independent model can yield $S_{\mathrm{obs}}>2$ by selection alone. We quantify the required setting dependence in total variation (TV) distance. For any reference law $\mu$ we prove the sharp bound $S_{\mathrm{obs}}\le 2+2{\sum }_{q\in Q}\mathrm{TV}({\nu }_q,\mu )$ for a CHSH quartet Q. Optimizing over $\mu$ yields the intrinsic dispersion bound $S_{\mathrm{obs}}\le 2+2{\Delta }_Q$, and, in particular, $S_{\mathrm{obs}}\le min\{4,2+6D_Q\}$, where $D_Q$ is the quartet TV diameter. The constants are optimal. Consequently, reproducing Tsirelson’s value $2\sqrt{2}$ within Bell-local measurement-independent models via setting-dependent acceptance requires ${\Delta }_Q\ge \sqrt{2}-1$ (hence, $D_Q\ge (\sqrt{2}-1)/3$). We then propose a two-lane experimental audit protocol: (i) prior-relative fair-sampling diagnostics using tags recorded on all trials, and (ii) prior-free dispersion diagnostics using accepted-tag distributions across settings, with ${\Delta }_{Q,X}$ computable by linear programming on finite tag alphabets. Full article

This paper identifies theoretical vulnerabilities in quantum integrity verification by demonstrating that Bell inequality (BI) violations, central to the detection of quantum entanglement, can align with predictions from hidden variable theories (HVTs) under specific measurement configurations. By invoking a Heisenberg-inspired measurement resolution constraint and finite-resolution positive operator-valued measures (POVMs), we identify “convergence vicinities” where the statistical outputs of quantum and classical models become operationally indistinguishable. These results do not challenge Bell’s theorem itself; rather, they expose a vulnerability in quantum integrity frameworks that treat observed Bell violations as definitive, experiment-level evidence of nonclassical entanglement correlations. We support our theoretical analysis with simulations and experimental results from IBM quantum hardware. Our findings call for more robust quantum-verification frameworks, with direct implications for the security of quantum computing, quantum-network architectures, and device-independent cryptographic protocols (e.g., device-independent quantum key distribution (DIQKD)). Full article

In device-independent (DI) quantum protocols, security statements are agnostic to the internal workings of the quantum devices—they rely solely on classical interactions with the devices and specific assumptions. Traditionally, such protocols are set in a non-local scenario, where two non-communicating devices exhibit Bell inequality violations. Recently, a new class of DI protocols has emerged that requires only a single device. In this setting, the assumption of no communication is replaced by a computational one: the device cannot solve certain post-quantum cryptographic problems. Protocols developed in this single-device computational setting—such as for randomness certification—have relied on ad hoc techniques, making their guarantees difficult to compare and generalize. In this work, we introduce a modular proof framework inspired by techniques from the non-local DI literature. Our approach combines tools from quantum information theory, including entropic uncertainty relations and the entropy accumulation theorem, to yield both conceptual clarity and quantitative security guarantees. This framework provides a foundation for systematically analyzing DI protocols in the single-device setting under computational assumptions. It enables the design and security proof of future protocols for DI randomness generation, expansion, amplification, and key distribution, grounded in post-quantum cryptographic hardness. Full article

We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the probability density as a function independent of the orientation of the measuring devices. Then, we use the dynamical evolution of the probability distribution to show that the spin-correlation integral cannot be expressed in terms of initial Cauchy data restricted to the particles. A measurement independence loophole ensues, which prevents the usage of the non-contextual correlation integrals required to demonstrate the CHSH-Bell inequality. We propose that correlated fields are the missing hidden variable triggering the coupled nonlinear oscillations of the particles, which bring about the synchronicities observed in the Einstein–Podolsky–Rosen–Bohm (EPRB) experiment. Full article

Two recent, prominent theorems—the “no-go theorem for observer-independent facts” and the “Local Friendliness no-go theorem”—employ so-called extended Wigner’s friend scenarios to try to impose novel, non-trivial constraints on the possible nature of physical reality. While the former is argued to entail that there can be no theory in which the results of Wigner and his friend can both be considered objective, the latter is said to place on reality stronger constraints than the Bell and Kochen–Specker theorems. Here, I conduct a thorough analysis of these theorems and show that they suffer from a list of shortcomings that question their validity and limit their strength. I conclude that the “no-go theorem for observer-independent facts” and the “Local Friendliness no-go theorem” fail to impose significant constraints on the nature of physical reality. Full article

This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connections among central factorial numbers, the Stirling numbers, and specific matrix inverses, and derives several closed-form formulas and inequalities. Additionally, this paper reveals new insights into the properties of these mathematical objects, including logarithmic convexity, explicit expressions for certain quantities, and identities involving the Bell polynomials of the second kind. Full article

In this work, we analyze recent proposals by Das and Dürr (DD) to measure the arrival time distributions of quantum particles within the framework of de Broglie Bohm theory (or Bohmian mechanics). We also analyze the criticisms made by Goldstein Tumulka and Zanghì (GTZ) of these same proposals, and show that each protagonist is both right and wrong. In detail, we show that DD’s predictions are indeed measurable in principle, but that they will not lead to violations of the no-signalling theorem used in Bell’s theorem, in contradiction with some of Das and Maudlin’s hopes. Full article

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as “non-classical”. The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell’s criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics. Full article

We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players’ point of view. Full article

Under the quaternion group, $Q_8$, spin helicity emerges as a crucial element of the reality of spin and is complementary to its polarization. We show that the correlation in EPR coincidence experiments is conserved upon separation from a singlet state and distributed between its polarization and coherence. Including helicity accounts for the violation of Bell’s Inequalities without non-locality, and disproves Bell’s Theorem by a counterexample. Full article

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of $\frac{1}{2}$—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of $\frac{1}{2}$, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q₈, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox. Full article

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems “conspiratorial”, in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell’s theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis. Full article

The Second Quantum Revolution refers to a contemporary wave of advancements and breakthroughs in the field of quantum physics that extends beyond the early developments of Quantum Mechanics that occurred in the 20th century. One crucial aspect of this revolution is the deeper exploration and practical application of quantum entanglement. Entanglement serves as a cornerstone in the ongoing revolution, contributing to quantum computing, communication, fundamental physics experiments, and advanced sensing technologies. Here, we present and discuss some of the recent applications of entanglement, exploring its philosophical implications and non-locality beyond Bell’s theorem, thereby critically examining the foundations of Quantum Mechanics. Additionally, we propose educational activities that introduce high school students to Quantum Mechanics by emphasizing entanglement as an essential concept to understand in order to become informed participants in the Second Quantum Revolution. Furthermore, we present the state-of-art developments of a largely unexplored and promising realization of real qubits, namely the molecular spin qubits. We review the available and suggested device architectures to host and use molecular spins. Moreover, we summarize the experimental findings on solid-state spin qubit devices based on magnetic molecules. Finally, we discuss how the Second Quantum Revolution might significantly transform law enforcement by offering specific examples and methodologies to address the evolving challenges in public safety and security. Full article