Related papers: Is Complex Probability Theory Consistent with Bell…
This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some…
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…
Einstein, Podolsky and Rosen (EPR) showed that it is possible to predict with certainty the value of a property without disturbing the object in question. In contrast, Quantum Mechanics (QM) holds that if different measurement setups cannot…
The failure of Bell's theorem for Clifford algebra valued local variables is further consolidated by proving that the conditions of remote parameter independence and remote outcome independence are duly respected within the recently…
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…
Bayes' rule $\mathbb{P}(B|A)\mathbb{P}(A)=\mathbb{P}(A|B)\mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through…
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
A simple analogy to understand the quantum-mechanical entanglement within local-realistic world is presented.
Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also some models based on non-local variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In…
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection…
In a old paper by G. Lochak, it is claimed that the Bell definition of a hidden variable is in conflict with the formalism of quantum mechanics. This result implies that it is not necessary to invoke non locality to explain the violation of…
Bell non-locality is a term that applies to specific modifications and interpretations of quantum mechanics. Yet, Bell's original 1964 theorem is often used to assert that unmodified quantum mechanics itself is non-local and that local…
For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local…
It is difficult to extract reliable criteria for causal locality from the limited ingredients found in textbook quantum theory. In the end, Bell humbly warned that his eponymous theorem was based on criteria that "should be viewed with the…
The aim of this paper is to give a sharp definition of Bell's notion of local causality. To this end, first we unfold a framework, called local physical theory, integrating probabilistic and spatiotemporal concepts. Formulating local…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…