scholarly journals MUTUAL INFORMATION OF BIPARTITE STATES AND QUANTUM DISCORD IN TERMS OF COHERENCE INFORMATION

2005 ◽  
Vol 03 (04) ◽  
pp. 691-728 ◽  
Author(s):  
FEDOR HERBUT
Keyword(s):  
Quantum Discord ◽  
Information Gain ◽  
Sufficient Conditions ◽  
Quantum Correlations ◽  
Global State ◽  
Final State ◽  
Global Coherence ◽  
State Formula ◽  
Necessary And Sufficient ◽  
Bipartite States

In relation to an observable and quantum state, the entity IC from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this paper, its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogating" the global state about the state of the opposite subsystem is derived with detailed entropy and information gain discussion. The apparent disappearance of discord in measurement is investigated, and it is shown that it is actually shifted from between subsystems 1 and 2 to between subsystems 1 and (2 + 3), where 3 is the measuring instrument. Finally, it is shown that the global coherence information IC(A2, ρ12) is shifted into the global coherence information [Formula: see text] in the final state [Formula: see text] of the measurement interaction.

scholarly journals Minimum Energy Control of 2D Positive Continuous-Discrete Linear Systems

2014 ◽  
Vol 8 (3) ◽  
pp. 165-168
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Final State ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
One Step ◽  
Necessary And Sufficient

Abstract The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.

CONTROLLABILITY OF A LINEAR DISCRETE SYSTEM WITH CHANGE OF THE STATE VECTOR DIMENSION

2021 ◽  
pp. 173-178
Author(s):  
V. V. Pichkur ◽  
D. A. Mazur ◽  
V. V. Sobchuk
Keyword(s):  
State Vector ◽  
Discrete System ◽  
Sufficient Conditions ◽  
The State ◽  
Functional Stability ◽  
Final State ◽  
Technological Processes ◽  
Linear Discrete System ◽  
Necessary And Sufficient ◽  
Vector Dimension

The paper proposes an analysis of controllability of a linear discrete system with change of the state vector dimension. We offer necessary and sufficient conditions of controllability and design the control that guarantees the decision of a problem of moving of such system to an arbitrary final state. It provides functional stability of technological processes described by a linear discrete system with change of the state vector dimension.

scholarly journals The selected problems of controllability of discrete-time switched linear systems with constrained switching rule

2015 ◽  
Vol 63 (3) ◽  
pp. 657-666 ◽  
Author(s):  
A. Babiarz ◽  
A. Czornik ◽  
J. Klamka ◽  
M. Niezabitowski
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Controllability Problem ◽  
Initial State ◽  
Final State ◽  
Switching Signal ◽  
Necessary And Sufficient ◽  
Time Linear

AbstractIn this paper the controllability problem for discrete-time linear switched systems is considered. The main goal is to find a control signal that steers any initial state to a given final state independently of the switching signal. In the paper, it is assumed that there are some constraints posed on the switching signal. Moreover, we present a necessary and sufficient conditions of some kinds of controllability. Three types of controllability, namely: from zero initial state to any final state, from any initial state to zero final state and from any initial state to any final state are considered. Finally, three illustrative examples are shown.

scholarly journals Method for finding a solution to a linear nonstationary interval ОDЕ system

2021 ◽  
Vol 17 (2) ◽  
pp. 148-165
Author(s):  
Аlexander V. Fominyh ◽  
◽  
Keyword(s):  
Original Problem ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Initial Position ◽  
Time Interval ◽  
Support Functions ◽  
Final State ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
The Given

The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. Оn the basis of these conditions, the method of the steepest descent is applied to the original problem. Some examples illustrate the constructed algorithm realization.

scholarly journals Non-monogamy of quantum discord and upper bounds for quantum correlation

2013 ◽  
Vol 13 (5&6) ◽  
pp. 469-478
Author(s):  
Xi-Jun Ren ◽  
Heng Fan
Keyword(s):  
Mutual Information ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Upper Bounds ◽  
Physical Analysis ◽  
Classical Correlation ◽  
Entanglement Of Formation ◽  
Quantum Mutual Information ◽  
Bipartite States

We consider a monogamy inequality of quantum discord in a pure tripartite state and show that it is equivalent to an inequality between quantum mutual information and entanglement of formation of two parties. Since this inequality does not hold for arbitrary bipartite states, quantum discord can generally be both monogamous and polygamous. We also carry out numerical calculations for some special states. The upper bounds of quantum discord and classical correlation are also discussed and we give physical analysis on the invalidness of a previous conjectured upper bound of quantum correlation. Our results provide new insights for further understanding of distributions of quantum correlations.

On the Final States of Shallow Arches on Elastic Foundations Subjected to Dynamical Loads

1968 ◽  
Vol 35 (4) ◽  
pp. 713-723 ◽  
Author(s):  
C. S. Hsu ◽  
C. T. Kuo ◽  
S. S. Lee
Keyword(s):  
Sufficient Conditions ◽  
Spatial Distributions ◽  
Time Varying ◽  
Final State ◽  
Shallow Arches ◽  
Elastic Foundations ◽  
Linear Elastic ◽  
Wide Range ◽  
Sinusoidal Shape ◽  
Necessary And Sufficient

Given in this paper is a nonlinear analysis of snap-through problems of shallow arches on linear elastic foundations subjected to time-varying loads which have a time-independent character as τ → ∞. Specific problems studied in detail are simply supported sinusoidal arches under impulsive loads, under time-varying loads with asymptotic spatial distributions of sinusoidal shape, and under time-varying loads with uniform asymptotic spatial distributions. It is found that for a very wide range of the foundation modulus a necessary and sufficient condition for stability against snap-through can be established and the final state of the arch predicted. Outside this range and when the loads are timewise step loads, useful sufficient conditions for instability and sufficient conditions for stability can be found separately. The nonlinear treatment presented here is exact in the sense that no approximation is made or is required in the mathematical analysis.

scholarly journals Reachability of standard and fractional continuous-time systems with constant inputs

2016 ◽  
Vol 26 (2) ◽  
pp. 147-159 ◽  
Author(s):  
Krzysztof Rogowski
Keyword(s):  
Continuous Time ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Final State ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
The Given ◽  
Time Linear ◽  
Order Continuous

Abstract The reachability of standard and fractional-order continuous-time systems with constant inputs is addressed. Positive and non-positive continuous-time linear systems are considered. Necessary and sufficient conditions for the existence of such constant inputs that steers the system from zero initial conditions to the given final state in desired time are derived and proved. As an example of such systems the electrical circuits with DC voltage sources are presented.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Sign in / Sign up

Export Citation Format

Share Document