No Arabic abstract
One of the major problems in quantum physics has been to generalize the classical root-mean-square error to quantum measurements to obtain an error measure satisfying both soundness (to vanish for any accurate measurements) and completeness (to vanish only for accurate measurements). A noise-operator based error measure has been commonly used for this purpose, but it has turned out incomplete. Recently, Ozawa proposed a new definition for a noise-operator based error measure to be both sound and complete. Here, we present a neutron optical demonstration for the completeness of the new error measure for both projective (or sharp) as well as generalized (or unsharp) measurements.
Recent years have witnessed a controversy over Heisenbergs famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics. We discuss two approaches to adapting the classic notion of root-mean-square error to quantum measurements. One is based on the concept of noise operator; its natural operational content is that of a mean deviation of the values of two observables measured jointly, and thus its applicability is limited to cases where such joint measurements are available. The second error measure quantifies the differences between two probability distributions obtained in separate runs of measurements and is of unrestricted applicability. We show that there are no nontrivial unconditional joint-measurement bounds for {em state-dependent} errors in the conceptual framework discussed here, while Heisenberg-type measurement uncertainty relations for {em state-independent} errors have been proven.
Bures distance holds a special place among various distance measures due to its several distinguished features and finds applications in diverse problems in quantum information theory. It is related to fidelity and, among other things, it serves as a bona fide measure for quantifying the separability of quantum states. In this work, we calculate exact analytical results for the mean root fidelity and mean square Bures distance between a fixed density matrix and a random density matrix, and also between two random density matrices. In the course of derivation, we also obtain spectral density for product of above pairs of density matrices. We corroborate our analytical results using Monte Carlo simulations. Moreover, we compare these results with the mean square Bures distance between reduced density matrices generated using coupled kicked tops and find very good agreement.
We introduce a new unconditionally solvable level-crossing two-state model given by a constant-amplitude optical field configuration for which the detuning is an inverse-square-root function of time. This is a member of one of the five families of bi-confluent Heun models. We prove that this is the only non-classical exactly solvable field configuration among the bi-confluent Heun classes, solvable in terms of finite sums of the Hermite functions. The general solution of the two-state problem for this model is written in terms of four Hermite functions of a shifted and scaled argument (each of the two fundamental solutions presents an irreducible combination of two Hermite functions). We present the general solution, rewrite it in terms of more familiar physical quantities and analyze the time dynamics of a quantum system subject to excitation by a laser field of this configuration.
Let Q_0 denote the rational numbers expanded to a meadow by totalizing inversion such that 0^{-1}=0. Q_0 can be expanded by a total sign function s that extracts the sign of a rational number. In this paper we discuss an extension Q_0(s ,sqrt) of the signed rationals in which every number has a unique square root.
In this paper we investigate the completeness of the Stark resonant eigenstates for a particle in a square-well potential. We find that the resonant state expansions for target functions converge inside the potential well and that the existence of this convergence does not depend on the depth of the potential well. By analyzing the asymptotic form of the terms in these expansions we prove some results on the relation between smoothness of target functions and the rate of convergence of the corresponding resonant state expansion.