Related papers: Solutions for the MaxEnt problem with symmetry con…
In this paper we discuss a master equation applied to the two level system of an atom and derive an exact solution to it in an abstract manner. We also present a problem and a conjecture based on the three level system. Our results may give…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
In this PhD thesis, several aspects regarding maximal entanglement are analyzed. In the first chapter, Bell Inequalities are analyzed from an operational perspective as well as novel Bell inequalities are obtained together with their…
The divergence condition is reformulated in the scaled boundary coordinates so as to prevent the spurious solutions in the finite element formulation.
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…
The entanglement measure for multiqudits is proposed. This measure calculates the partial entanglement distributed by subsystems and the complete entanglement of the total system. This shows that we need to measure the subsystem…
In this paper, we find the necessary and sufficient condition for the maximal entanglement of the state, $ |\psi>=\mu|\alpha>|\beta>+\lambda|\alpha>|\delta>+ \rho|\gamma>|\beta>+\nu|\gamma>|\delta>,$ constructed by linearly independent…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit…
We consider the degrees of controllability of multi-partite quantum systems as well as necessary and sufficient criteria for each case. The results are applied to the problem of simultaneous control of an ensemble of quantum dots with a…
An expression is proposed for the quantum mechanical state of a pre- and post-selected ensemble, which is an ensemble determined by the final as well as the initial state of the quantum systems involved. It is shown that the probabilities…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
We obtain a bound on the number of solutions of $x^q=x$ in a finite noncommutative algebra over a field with $q$ elements. Furthermore, we completely characterize those rings for which this maximum number is attained.
We address the problem of the minus sign sampling for two electron systems using the path integral approach. We show that this problem can be reexpressed as one of computing free energy differences and sampling the tails of statistical…
In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems…
Quantum dots (QDs) are one of the promising candidates of interconnection between electromagnetic field and electrons in solid-state devices. Dark states appear as a result of coherence between the electromagnetic fields and the discrete…