The Influence Of Quantum Channels On The Coherence And Maximally Steered Coherence

Quantum coherence is a way of describing quantum states.Quantum states can be divided into free states and coherent states,meanwhile,quantum operations can be divided into free operations and coherent operations.Quantum coherence is a crucial resource in quantum information theory,and it is the foundation of many quantum theories.Quantum steering is originally considered by Schrodinger,and has also recently received much attention.Based on these dissertations and the methods in operator theory and matrix theory,this paper define the maximally steered coherence of quantum states,and discuss some properties of quantum co-herence and the maximally steered coherence of quantum states.Meanwhile,we research the impacts of quantum channels on quantum coherence and the influences of local quantum channels on the maximally steered quantum coherence of quantum states.This article is divided into four chapters and arranged as follows:In Chapter 1,we introduce some research significance and current situation about our main contents.Moreover,some basic notations,concepts and theorems are listed.In Chapter 2,we study the influence of the quantum channels on the coherence.To begin with,the coherent properties of product states are discussed.Besides,it is proved that the partial trace operation and genuinely incoherent quantum channels do not increase the quantum coherence.Meanwhile,it is proved that diagonal unitary channels do not change the quantum coherence.In Chapter 3,we research the influence of local quantum channels on the max-imally steered coherence.At first,we define the maximally steered coherence of a quantum state.Moreover,it is proved that the maximally steered coherence of any quantum state is 0 if and only if the state is classically correlated.Next,some sufficient or necessary conditions for local quantum channels to breaking,increasing or decreasing maximally steered coherence are obtained,respectively.Finally,the unitary operation does not change the maximally steered coherence of quantum s-tate.Finally,the upper bound of maximally steered coherence for any quantum state is obtained.