Related papers: Negative Probabilities, Fine's Theorem and Linear …
A characterization of noncontextual models which fall within the ambit of Fine's theorem is provided. In particular, the equivalence between the existence of three notions is made explicit: a joint probability distribution over the outcomes…
In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions…
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…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from…
Negative probabilities emerged at intermediate steps in various attempts to predict the distributions of quantum interference. There is no consensus on their meaning yet. It has been suggested (Khrennikov, 1998) that negative probabilities…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of…
We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT.…
It is shown that Bell's counterfactuals admit joint quasiprobability distributions (i.e. joint distributions exist, but may not be non-negative). A necessary and sufficient condition for the existence among them of a true probability…
Density matrices are the most general descriptions of quantum states, covering both pure and mixed states. Positive semidefiniteness is a physical requirement of density matrices, imposing nonnegative probabilities of measuring physical…
Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has…
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different…
Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for the position and momentum. Most notably, they both give correct one-dimensional marginal probability…
Probability is distinguished into two kinds: physical and epistemic, also, but less accurately, called objective and subjective. Simple postulates are given for physical probability, the only novel one being a locality condition. Translated…
This paper establishes a direct, robust and intimate connection between (i) non classicality tests for various quantum features, e.g., non-Boolean logic, quantum coherence, nonlocality, quantum entanglement, quantum discord; (ii) negative…
We explain, on the example of Wigner's quasiprobability distribution, how negative probabilities may be used in the foundations of probability.
Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled…