Related papers: The quantum phase problem: steps toward a resoluti…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the…
A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have…
Generalized Weyl quantization formalism for the cylindrical phase space $S^1 \times \mathbb{R}^1$ is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
I would claim that we do not have a suitably general definition of what a topological phase is, or more importantly, any robust understanding of how to enter one even in the world of mathematical models. The latter is, of course, the more…
The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system…
W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
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…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
Standard quantization using, for example, path integration of field theory models, includes paths of momentum and field reach infinity in the Hamiltonian density, while the Hamiltonian itself remains finite. That fact causes considerable…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The phase resolution of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles N, a 1/sqrt{N} improvement over the…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…