Information-Theoretic Meaning of Quantum Information Flow and Its Applications to Amplitude Amplification Algorithms

The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of analyzing and quantifying loss or gain of information on a quantum system when the system interacts with its environment. We show that the information flow, the theoretical method of characterizing (non-)Markovianity of quantum dynamics, corresponds to the rate of the minimum uncertainty about the system given quantum side information. Thereafter, we analyze the information exchange among subsystems that are under the performance of quantum algorithms, in particular, the amplitude amplification algorithms where the computational process relies fully on quantum evolution. Different realizations of the algorithm are considered, such as i)quantum circuits, ii) analog computation, and iii) adiabatic computation. It is shown that, in all the cases, our formalism provides insights about the process of amplifying the amplitude from the information flow or leakage on the subsystems.Comment: 7 pages, 5 figures, close to the published versio

Theoretical Models of the Brans-Dicke Parameter for Time Independent Deceleration Parameters

The dependence of the dimensionless Brans-Dicke (BD) coupling parameter upon time and the scalar field has been determined, for an isotropic and homogeneous space of zero curvature, by solving BD field equations and the wave equation for the scalar field. For this purpose, very simple expressions of empirical scale factors, that generate constant deceleration parameters, have been used here in two theoretical models. The characteristics of time dependence of the BD parameter, obtained from these two models, are in qualitative agreement with each other. The mathematical expressions representing the rate of change of the BD parameter with time, based on these two models, are found to have identical forms. Combining the expressions of the BD parameter obtained from these two models, a method of determination of the present value of the equation-of-state (EoS) parameter of the cosmic fluid has been discussed. Its value is found to be consistent with the ranges of values obtained from other studies based on recent observations

Time Variation of the Matter Content of the Expanding Universe in the Framework of Brans-Dicke Theory

In the framework of Brans-Dicke theory, a cosmological model regarding the expanding universe has been formulated by considering an inter-conversion of matter and dark energy. A function of time has been incorporated into the expression of the density of matter to account for the non-conservation of the matter content of the universe. This function is proportional to the matter content of the universe. Its functional form is determined by using empirical expressions of the scale factor and the scalar field in field equations. This scale factor has been chosen to generate a signature flip of the deceleration parameter with time. The matter content is found to decrease with time monotonically, indicating a conversion of matter into dark energy. This study leads us to the expressions of the proportions of matter and dark energy of the universe. Dependence of various cosmological parameters upon the matter content has been explored

Theoretical Models of the Brans-Dicke Parameter for Time Independent Deceleration Parameters

The dependence of the dimensionless Brans-Dicke (BD) coupling parameter upon time and the scalar field has been determined, for an isotropic and homogeneous space of zero curvature, by solving BD field equations and the wave equation for the scalar field. For this purpose, very simple expressions of empirical scale factors, that generate constant deceleration parameters, have been used here in two theoretical models. The characteristics of time dependence of the BD parameter, obtained from these two models, are in qualitative agreement with each other. The mathematical expressions representing the rate of change of the BD parameter with time, based on these two models, are found to have identical forms. Combining the expressions of the BD parameter obtained from these two models, a method for the determination of the present value of the equation-of-state (EoS) parameter of the cosmic fluid has been discussed. Its value is found to be consistent with the ranges of values obtained from other studies based on recent observations

Time Evolution of Density Parameters for Matter and Dark Energy and their Interaction Term in Brans-Dicke Gravity

In the framework of Brans-Dicke (BD) theory, the first part of the present study determines the time dependence of BD parameter, energy density and equation of state (EoS) parameter of the cosmic fluid in a universe expanding with acceleration, preceded by a phase of deceleration. For this purpose, a scale factor has been chosen such that the deceleration parameter, obtained from it, shows a signature flip with time. Considering the dark energy to be responsible for the entire pressure, the time evolution of energy parameters for matter and dark energy and the EoS parameter for dark energy have been determined. An effective interaction term, between matter and dark energy, has been proposed and calculated. Its negative value at the present time indicates conversion of matter into dark energy. Using this term, the time dependence of the rates of change of matter and dark energy has been determined. It is found that the nature of dependence of the scalar field upon the scale factor plays a very important role in governing the time evolution of the cosmological quantities studied here. The present study provides us with a simple way to determine the time evolution of dark energy for a homogeneous and isotropic universe of zero spatial curvature, without involving any self-interaction potential or cosmological constant in the formulation.Comment: 22 pages, 16 figures, 2 tables. In the present version we have two models of density parameter calculation. Calculations of time derivatives of densities have been added to the previous version. Four new graphs have been added to the older version. Changes have been made to different sections of this articl

Beating no-go theorems by engineering defects in quantum spin models

There exist diverse no-go theorems, ranging from no-cloning to monogamies of quantum correlations and Bell inequality violations, which restrict the processing of information in the quantum world. In a multipartite scenario, monogamy of Bell inequality violation and exclusion principle of dense coding are such theorems, which impede the ability of the system to have quantum advantage between all its parts. In ordered spin systems, the twin restrictions of translation invariance and monogamy of quantum correlations, in general, enforce the bipartite states to be neither Bell inequality violating nor dense-codeable. We show that these quantum characteristics, viz. Bell inequality violation and dense-codeability, can be resurrected, and thereby the no-go theorems overcome, by having quenched disorder in the system parameters leading to quantum spin glass or quantum random field models. We show that the quantum characteristics are regained even though the quenched averaging keeps the disordered spin chains translationally invariant at the physically relevant level of observables. The results show that it is possible to conquer constraints imposed by quantum mechanics in ordered systems by introducing impurities.Comment: 9 pages, 6 figures, RevTeX 4.