Related papers: Contextual logic for quantum systems
Contextuality has been conjectured to be a super-classical resource for quantum computation, analogous to the role of non-locality as a super-classical resource for communication. We show that the presence of contextuality places a lower…
Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a…
The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on…
We study analysis of complex systems using a Quantitative Theory of Meaning developed as an extention of Shannon's Communication Theory. The approach consideres complexity not in terms of the manifestation of its effects which are…
A set of quantum measurements exhibits quantum contextuality when any consistent value assignment to the measurement outcomes leads to a contradiction with quantum theory. In the original Kochen-Specker-type of argument the measurement…
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, understood as a resource for quantum computation, it…
Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we…
Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any…
Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
Quantum computers promise dramatic advantages over their classical counterparts, but the answer to the most basic question "What is the source of the power in quantum computing?" has remained elusive. Here we prove a remarkable equivalence…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
I show how space-like structures emerge within the topos-based approach to quantum mechanics. With a physical system, or, more generally, with an operationalistic setup a context category is associated being in fact an ordered collection of…
A projective quantum logic in terms of relative states is developed, emphasizing the importance of information transfer between a system under study and its environment. The need for accounting for the historical evolution of system is…
The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges…
Contextuality has long been associated with topological properties. In this work, such a relationship is elevated to identification in the broader framework of generalized contextuality. We employ the usual identification of states,…