Density Operators

Riccardo Manenti, Mário Motta

Abstract The first part of the chapter is devoted to the discussion of density operators. We first introduce the definition of a density operator and the unitary evolution of a quantum state. We then examine the measurement of a quantum system using the density operator approach. We present the density operator associated with a qubit and a harmonic oscillator at thermal equilibrium. The second part of the chapter focuses on bipartite systems. We show that the quantum state of a subsystem is given by the partial trace of the density operator of the global system. Finally, we explain the concept of purification of a density operator

Muhammad F. Emzir, Ian R. Petersen, Matthew J. Woolley

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of having multiple isolated invariant density operators. We then show how to analyze the stability of this set via a candidate Lyapunov operator.

Włodzimierz M. Tulczyjew

It is widely believed that statistical interpretation of quantum mechanics requires that density operators representing quantum states be normalized. We present a description of selective measurements in terms of density operators. The description is inspired by Schwinger's Algebra of Microscopic Measurements. Density operators used are not normalized. We do not know applications of density operators requiring normalization.