Related papers: On the Relativity of Quantumness as Implied by Rel…
By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these…
An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…
Czachor's model of hierarchical arithmetics begins with a valid formal premise but fixes the key probability mapping g by importing the Born rule and Fubini-Study metric from standard quantum mechanics, where Born probabilities are…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…
To begin, we find certain formulas $Q(k,\alpha)= G_1^k(\alpha) G_2^k(\alpha)$, for $k = -1, 0, 1,...,9$. These yield that part of the total separability probability, $P(k,\alpha)$, for generalized (real, complex, quaternionic,\ldots)…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to…
We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-$\frac12$ particles. The class of correlations…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
Taking quantum formalism as a point of reference and connection, we explore the various possibilities that arise in the construction of physical theories. Analyzing the distinct physical phenomena that each of them may describe, we…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in…
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal…
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…