Related papers: Observing a Changing Hilbert-Space Inner Product
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
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…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
We provide an overview of standard "projective" quantum measurements with the goal of elucidating connections between theory and experiment. We make use of a unitary "Stinespring" representation of measurements on a dilated Hilbert space…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a…
The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This…
In the statement "The vector is an element of the closed linear subspace of the Hilbert space H", the predicate "... is an element of ..." might be not only determined, that is, either true or false (depending on whether set membership is…
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…
It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…
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…
A new type of gauge quantum theory (superrelativity) has been proposed. This differs from ordinary gauge theories in sense that the affine connection of our theory is constructed from first derivatives of the Fubini-Study metric tensor.…
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…
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities…