Related papers: State property systems and orthogonality
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
In this article, we generalize the notion of orthogonality as a linear combination of norm derivatives in order to give a novel concept that we refer to as $\rho_{\alpha,\beta}$-orthogonality. Also, we discuss some of its geometric…
We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated…
An orthoset (also called an orthogonality space) is a set $X$ equipped with a symmetric and irreflexive binary relation $\perp$, called the orthogonality relation. In quantum physics, orthosets play a central role. In fact, a Hilbert space…
Quantum entanglement obscures the notion of local operations; there exist quantum states for which all local actions on one subsystem can be equivalently realized by actions on another. We characterize the states for which this fundamental…
The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…
We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper…
We discuss some fundamental properties of discrete system-time history states. Such states arise for a quantum reference clock of finite dimension and lead to a unitary evolution of system states when satisfying a static discrete…
Statistically interpretable axioms are formulated that define a quantum stochastic process (QSP) as a causally ordered operator field in an arbitrary space-time region T of an open quantum system under a sequential observation at a discrete…
We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and…
It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to…
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…
Despite significant work on resource estimation for quantum simulation of electronic systems, the challenge of preparing states with sufficient ground state support has so far been largely neglected. In this work we investigate this issue…
Space of states of PT symmetrical quantum mechanics is examined. Requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to the space with an indefinite metric. The self…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
The quantum superposition principle has been extensively utilized in the quantum mechanical description of the bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of…
The different time-dependent distances of two arbitrarily close quantum or classical-statistical states to a third fixed state are shown to imply an experimentally relevant notion of state sensitivity to initial conditions. A quantitative…