Related papers: On Quantum States for angular Position and Angular…
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any…
In certain circumstances, the uncertainty, $\Delta S [\phi]$, of a quantum observable, $S$, can be bounded from below by a finite overall constant $\Delta S>0$, \emph{i.e.}, $\Delta S [\phi] \geq \Delta S$, for all physical states $\phi$.…
The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical…
This is a pedagogical paper where we present a physically motivated approach to introduce the coherent states of a harmonic oscillator from which it is simple to rigorously derive their mathematical definition. We do this in two different…
Complex techniques of general relativity are used to determine \emph{all} the states in the two and three dimensional momentum spaces in which the equality holds in the uncertainty relations for the non-commuting basic observables of…
In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…
The measurement of quantum states is one of the most important problems in quantum mechanics. We introduce a quantum state tomography technique in which the state of a qubit is reconstructed, while the qubit remains undetected. The key…
We consider a system of two particles, each with large angular momentum $j$, in the singlet state. The probabilities of finding projections of the angular momenta on selected axes are determined. The generalized Bell inequalities involve…
Uncertainty relations $\Delta(\rho)\ge \eta_d$ in terms of the Gini index are studied. The `Gini uncertainty constant' $\eta_d$ is estimated numerically and compared to an upper bound $\tilde \eta_d\ge \eta_d$. It is shown that for large…
An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is…
The main subject of the paper is the description of unstable states in quantum mechanics and quantum field theory. Unstable states in quantum field theory can only be introduced as the intermediate states and not as asymptotic states. The…
We propose and experimentally verify a scheme to engineer arbitrary states of traveling light field up to the two-photon level. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means…
The state function of a quantum object is undetermined with respect to its phase. This indeterminacy does not matter if it is global, but what if the components of the state have unknown relative phases? Can useful computations be performed…
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…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum…
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 consider quantum mechanics on the noncommutative plane in the presence of magnetic field $B$. We show, that the model has two essentially different phases separated by the point $B\theta=c\hbar^2/e$, where $\theta$ is a parameter of…