Research On Quantum Correlation Of A Pair And A Sequence Of Quantum Ensembles

As an important resource in quantum information processing, quantum entan-glement is an essential feature in quantum mechanics. Recently, with the develop-ment of quantum information theory, some people found that quantum correlations could play an important role on many quantum information processing tasks with-out entanglement, so it becomes a hot topic in quantum information. In quantum information theory, a quantum state of a quantum system lies in some state pi at a certain probability pi through a quantum measurement. Thus, quantum states Pi,p2,...,pn and corresponding probabilities P1,P2,...,Pn are obtained and so an ensemble ε={pi,ρi}in=1 is presented. In this paper, the basic thought of quantum correlation is introduced firstly and quantum correlation contained in a pair{ρ, η} of quantum ensembles and a sequence{ε1, ε2,..., εn} of quantum ensembles is studied and computed. To do this, a 4-partite quantum state ρε,η and a 2n-partite quantum state ρε1,ε2,...,εn are constructed. Based on quantum relative entropy, two measure functions are defined in order to reveal the quantum correlation of the pair and the sequence. Some properties of the two measure functions are proved by using the methods in operator algebra and operator theory. This article is divided into three chapters and arranged as follows:In Chapter 1, we introduce some research background and status on our main contents, definitions and theorems.In Chapter 2, we study the characterization and quantification of a pair{ρ,η} of quantum ensembles. Firstly, we introduce the related basic concepts of quantum correlation. Secondly, based on the characterization and quantification of a single quantum state and a quantum ensemble, we construct a 4-partite quantum state ρε,η to describe quantum correlation a pair of quantum ensembles. Then by using the quantum relative entropy, a measure function is defined in order to reveal the quantum correlation of a pair of quantum ensembles. Finally, we discuss some prop-erties of the measure function and the equivalence of a pair of quantum ensembles being a pair of classical ensembles.In Chapter 3, we study the characterization and quantification of a sequence {ε1,ε2),...,ε} of quantum ensembles. Firstly, we introduce the related basic con-cepts. Nextly, based on the method of using for revealing quantum correlation of a pair of quantum ensembles in second chapter, we construct a measure function to reveal quantum correlation of a sequence of quantum ensembles. Some properties of the measure function are proved.