Related papers: Is the Quantum State Real in the Hilbert Space For…
The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum…
The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
The determination of the quantum state of a single system by protective observation is used to justify operationally a formulation of quantum theory on the quantum state space (projective Hilbert space) $\cal P$. Protective observation is…
Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus…
The main claim of the paper is that one can be 'realist' (in some sense) about quantum mechanics without requiring any form of realism about the wave function. We begin by discussing various forms of realism about the wave function, namely…
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement independent reality of the system. The most simple case is observed in a three-dimensional…
Despite their inextricable quantum mechanical nature, events at a high energy particle collider experiment typically have very few unambiguous quantum signatures, due the type of data and the manner in which they are collected. We present a…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
The physical nature of any quantum source guarantees the existence of an effective Hilbert space of finite dimension, the physical sector, in which its state is completely characterized with arbitrarily high accuracy. The extraction of this…
Motivated in part by John Wheeler's assertion that the continuum nature of Hilbert Space conceals the `it-from-bit' information-theoretic character of the quantum wavefunction, a theory of quantum physics (Rational Quantum Mechanics - RaQM)…
After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics…
The notion of state vector is, in quantum mechanics, as central as it is problematic, as illustrates the wealth of publications about the sub- jects, including in particular the many attempts to obtain an acceptable interpretation of…
A reasonable explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view a quantum particle is an objectively real wave packet consisting of irregular…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
A conceptual difficulty in the foundations of quantum mechanics is the quantum measurement problem (QMP), essentially concerned with the apparent non-unitarity of the measurement process and the classicality of macroscopic systems. In an…
There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational…