Related papers: Negative Probabilities, Fine's Theorem and Linear …
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. A quantum theory of closed systems requires two elements; 1) a condition specifying which sets of histories may…
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH…
The celebrating theorem of A. Fine implies that the CHSH inequality is violated if and only if the joint probability distribution for the quadruples of observables involved the EPR-Bohm-Bell experiment does not exist, i.e., it is impossible…
In the consistent histories (CH) approach to quantum theory probabilities are assigned to histories subject to a consistency condition of negligible interference. The approach has the feature that a given physical situation admits multiple…
We present a new framework for creating a quantum version of a classical game, based on Fine's theorem. This theorem shows that for a given set of marginals, a system of Bell's inequalities constitutes both necessary and sufficient…
In this paper we discuss quantum-like decision-making experiments using negative probabilities. We do so by showing how the two-slit experiment, in the simplified version of the Mach-Zehnder interferometer, can be described by this…
In this paper we attempt to establish a theory of negative (quasi) probability distributions from fundamental principles and apply it to the study of the double-slit experiment in quantum mechanics. We do so in a way that preserves the main…
Bell's theorem shows that no hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this work we demonstrate that by…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite…
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…
We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…
In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in…
Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…
A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require…
I consider the "Quantum Bayesian" view of quantum theory as expounded in a 2006 paper of Caves, Fuchs, and Schack. I argue that one can accept a generally personalist, decision-theoretic view of probability, including probability as…
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the…
Nonnegative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories. The resulting {\it linearly positive histories} avoid the highly restrictive decoherence conditions and…
Negative probabilities have long been discussed in connection with the foundations of quantum mechanics. We have recently shown that, if signed measures are allowed on the hidden variables, the class of probability models which can be…
Motivated by real-world situations found in high energy particle physics, we consider a generalisation of the likelihood-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. By extension, this…