Related papers: Reconstructing quantum theory from its possibilist…
Given a quantum state in the finite-dimensional Hilbert space $ \C^n $, the range of possible values of a quantum observable is usually identified with the discrete spectrum of eigenvalues of a corresponding Hermitian matrix. Here any such…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
We use the Gazeau-Klauder formalism to construct coherent states of non-Hermitian quantum systems. In particular we use this formalism to construct coherent state of a PT symmetric system. We also discuss construction of coherent states…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…
Establishing a notion of the quantum state that applies consistently across space and time could be a crucial step toward formulating a relativistic quantum theory. We give an operational meaning to multipartite quantum states over…
Quantum mechanics describes seemingly paradoxical relations between the outcomes of measurements that cannot be performed jointly. In Hilbert space, the outcomes of such incompatible measurements are represented by non-orthogonal states. In…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
Masanes, Galley and M\"uller [1] argue that the measurement postulates of non-relativistic quantum mechanics follow from the structural postulates together with an assumption they call the "possibility of state estimation". Their argument…
We combine the ideas of Dirac's orthonormal representation, Everett's relative state, and 't Hooft's ontological basis to define the notion of a world for quantum mechanics. Mathematically, for a quantum system $\mathcal{Q}$ with an…
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…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
An operational definition of contextuality is introduced which generalizes the standard notion in three ways: (1) it applies to arbitrary operational theories rather than just quantum theory, (2) it applies to arbitrary experimental…
We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context…
C. A. Fuchs and M. Sasaki defined the quantumness of a set of quantum states in \cite{Quantumness}, which is closely related to the fidelity loss in transmission of the quantum states through a classical channel. In \cite{Fuchs}, Fuchs…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…