Editorial: Quantum information theory

influences-faster than the speed of light-which contradicted the spirit of Einstein's relativity and which Einstein famously described as "spooky." Recognizing the extraordinary implications of his claim, Bell emphasized the necessity of definitive experimental proof that photonpair measurements could not influence one another through any signal propagating at or below the speed of light. Alain Aspect and his collaborators provided a groundbreaking solution by developing experiments that rapidly switched polarizer angles in between measurement, ensuring that the actual pair-measurements could not influence each other within the light-speed limit.These fast-switching experiments were later refined by research groups led by Alain Aspect, John Clauser, and Anton Zeilinger-whose team even conducted photon-pair measurements between distant Canary Islands. Their collective achievements were recognized with the 2022 Nobel Prize in Physics. In their Nobel lectures, they emphasized Bell's postulated quantum nonlocalities. Many researchers have since endorsed this interpretation, arguing that such instantaneous influences underpin the computational advantages of quantum systems. However, no direct empirical proof of this claim exists, and Bell's theoretical framework remains the principal foundation for associating quantum superposition with nonlocality. Consequently, Bell's inequalities have become a central defense against more conventional, Einsteinian interpretations of quantum phenomena. Despite extensive experimental progress, substantial doubts remain concerning the theoretical soundness of Bell's framework-doubts that extend well beyond the familiar experimental loopholes. These reservations center on the mathematical consistency of Bell-type derivations, as numerous previously neglected mathematical and physical factors have been identified that can yield violations of Belltype inequalities. The introduction of rapid polarizer switching partially mitigated these concerns by not only ensuring that photon pairs emitted at the source could not depend on the polarizer settings, but also by suggesting that the observing experimenters (conventionally named Alice and Bob) are spatially separated, mutually unaware of each other's settings, and free to choose their polarizer orientations independently. Under these conditions, explanations of the observed correlations seem to necessarily invoke instantaneous, nonlocal influences. The analyses presented in this section challenge that conclusion, showing, for example, that such reasoning implicitly disregards the stratagems of Einstein's theory of relativity. Yes, Alice and Bob are causally disconnected during the pair-measurement process and cannot possibly perform any mutual or relative assessment of outcomes in real time. However, a relative assessment may be carried out by theoreticians who retrospectively can check the consistency of their model -after all measurement data have been collected. Gerard 't Hooft identified fundamental problems in Bell's framework early on and consistently expressed skepticism toward prevailing interpretations involving quantum superposition. Despite his distinguished reputation and profound contributions to theoretical physics, his deterministic perspective was largely disregarded and, at times, unfairly associated with "conspiratorial" thinking. This section includes one of 't Hooft's important papers, which demonstrates that the standard quantum-mechanical harmonic oscillator possesses an exact duality with a fully classical system, thereby revealing the potential existence of hidden ontological variables-a possibility often denied in textbooks emphasizing Bell's conclusions. 't Hooft's ideas and findings indicate the need for a more extensive investigation into underlying classical variables that are more basic than the quantum variables usually employed.Several other contributions in this section further demonstrate that Bell's work possesses only limited validity and cannot be exclusively grounded in considerations of locality or determinism. Karl Hess and Jürgen Jakumeit show that crucial mathematical details within set-theoretic probability frameworks were neglected by Bell and his followers, despite their importance for the validity of Bell-type proofs. From a mathematical standpoint, the cardinality of the number M of Einstein's "elements of reality" (the properties of entangled photons) relative to the number N of measurements determines whether Bell-type proofs hold; they do so only when M≪N. This insight also clarifies the success of Mermin's well-known elementary proofs, which typically assume M=8. There is, however, no physical justification for restricting the number of photon-pair properties to eight. Hess and Jakumeit further point out that for finite M, Bell-type inequalities can only be derived by neglecting the physically necessary symmetry associated with the invariance of average measurement outcomes under certain polarizer rotations.Marian Kupczynski promotes a statistical interpretation of quantum mechanics and critically reexamines Bell's theorem and its implications. Drawing upon Bertrand's paradox, he emphasizes the contextual nature of probabilities and their intrinsic dependence on the specific experimental conditions and measurement protocols. Kupczynski argues that if one introduces additional setting-dependent local variables-representing the physical characteristics of measuring instruments and procedures-into Bell's probabilistic framework, then quantum correlations can be accounted for without invoking nonlocalities. Kupczynski's explanation also relies on the invariance of certain global physical laws with respect to rotations of the coordinate system employed to describe the EPR experiments, thereby guaranteeing consistency with the observed quantum statistics. His conclusions are extensively supported by numerous references in his review, which collectively reinforce the contextual and statistical foundations of his interpretation.Taken together, these analyses suggest that while the 2022 Nobel Prize recognized remarkable experimental achievements, its interpretative emphasis on instantaneous influences and quantum superposition may have led the field astray. The use of Bell-type inequalities by Aspect, Clauser, and Zeilinger remains conceptually problematic. The photon-pair entanglement-experiments described by Carl Kocher can, in fact, be interpreted consistently with Einstein's notion of physical reality. Kocher's contribution in this section elucidates the essential details of the first EPR experiment with entangled photons and provides clear explanations of the factors underlying entanglement.The contribution by Ana Maria Cetto and Luis de la Peña offers an additional compelling rationale to reconsider quantum-mechanical interpretations by taking the underlying physics of quantum phenomena into account. They establish a link between particle spin and quantum statistics, which results from the particles' response to the shared background radiation field. This approach has significant implications for understanding entanglement.Finally, Theodorus Maria Nieuwenhuizen's paper presents a rigorous Hamiltonian treatment of the Curie-Weiss measurement model for spin-1 systems, distinguishing the stages of dephasing, decoherence, and registration. The associated H-theorem for the "dynamical free energy" illustrates relaxation toward a stable pointer state. This ensemble-based treatment, in which the density matrix becomes diagonal, provides valuable insight into the quantum measurement problem, without solving it.