Some Notes On Quantum Coherence And Quantum Steering

Quantum nonlocality is one of the most prominent features that distinguish the quantum theory from the classical physics.It serves as the central resource in quan-tum information processing.Quantum nonlocality manifests itself in three forms:quantum entanglement,quantum steering and Bell nonlocality.Quantum steering is a kind of important quantum nonlocality which was proposed by Schrodinger in the study of the EPR paradox,it describes the effecting ability of measuring on one par-ticle to another which can't be explained by LHS.Quantum steering is a quantum correlation between quantum entanglement and quantum nonlocality.And quan-tum coherence is one of the most important properties of quantum mechanics,and it is also the necessary condition of quantum correlation.It is the key element of a series of physical phenomena,many quantum resource theories are based on it.Recently,the duality quantum computer and the mutually unbiased measure-ment have attracted much more attention,and more discussions and applications have been shown.In this paper,based on the theory of the duality quantum com-puter and the mutually unbiased measurement,we discuss the quantum coherence of duality quantum computers and the quantum steering of mutually unbiased mea-surements.In Chapter 1,we introduce some symbolic representation and give some basic notation,concept and theorems of the quantum coherence and the quantum steering.Moreover,the research significance and current situation about our main content have been listed.In Chapter 2,we give some properties of the quantum coherence and the d-uality quantum computer,on this foundation,we study the coherence of output states under general unitary operators,incoherence unitary operators and unitary permutation operators with the same input state.In Chapter 3,based on the study of some properties of the quantum steering and the mutually unbiased measurements,we discuss the quantum steering of sep-arable states,pure entangled states and special Bell-diagonal states under mut ually unbiased measurements.