Related papers: A Representation for Compound Quantum Systems as I…
We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
We consider three types of entities for quantum measurements. In order of generality, these types are: observables, instruments and measurement models. If $\alpha$ and $\beta$ are entities, we define what it means for $\alpha$ to be a part…
We generalize the results of [B. Coecke, Helv. Phys. Acta 68, 396 (1995)] for the representation of coherent states of a spin-1 entity to spin-S entities with S>1 and to non-coherent spin states: through the introduction of 'hidden…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
We work out a quantum-theoretic model in complex Hilbert space of a recently performed test on co-occurrencies of two concepts and their combination in retrieval processes on specific corpuses of documents. The test violated the…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
Our investigation aims to study the specific role played by entanglement in the quantum computation process, by elaborating an entangled spin model developed within the 'hidden measurement approach' to quantum mechanics. We show that an…
There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We explore a new class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing…
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…
We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence…