Related papers: Epistemic Odds of Contextuality in Cyclic Systems
Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical…
Different analytic notions of contextuality fall into two major groups: probabilistic and strong notions of contextuality. Kochen and Specker's Theorem~0 is a demarcation criterion for differentiating between those groups. Whereas…
We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104 240401 (2010)]. The theory of contextual values extends the well-established theory…
Bell's theorem prompts us with a fundamental inquiry: what is the simplest scenario leading to the incompatibility between quantum correlations and the classical theory of causality? Here we demonstrate that quantum non-classicality is…
Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on pre- and post-selected quantum systems. A class of such effects, which we call ``logical pre- and post-selection paradoxes'', bear a…
A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and…
We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong…
Quantum mechanics allows only certain sets of experimental results (or "probabilistic models") for Bell-type quantum non-locality experiments. A derivation of this set from simple physical or information theoretic principles would represent…
We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal models that allow for cycles, latent…
An operational definition of contextuality is introduced which generalizes the standard notion in three ways: (1) it applies to arbitrary operational theories rather than just quantum theory, (2) it applies to arbitrary experimental…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…
We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal…
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…
Contextuality describes the nontrivial dependence of measurement outcomes on particular choices of jointly measurable observables. In this work we review and generalize the bundle diagram representation introduced in [S. Abramsky et al.,…
Kochen-Specker contextuality is a fundamental feature of quantum mechanics and a crucial resource for quantum computational advantage and reduction of communication complexity. Its presence is witnessed in empirical data by the violation of…
We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…
How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with…
Recent experiments have shown that nature violates noncontextual inequalities regardless of the state of the physical system. So far, all these inequalities involve measurements of dichotomic observables. We show that state-independent…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…