Coherence Studies Of Quantum Superposition States

Quantum coherence arising from quantum superposition,which is the important basic resources in quantum information processing.Quantum coherence plays an important role in quantum computation,such as Deutsch algorithm,Shor algorithm,Grover algorithm and quantum circuit and so on.Researches show that quantum coherence plays a vital role in quantum thermodynamics,quantum algorithms,quantum metrology,quantum channels resolution and quantum biology.Baumgratz et al.proposed a resource theoretical framework for quantifying quantum coherence in 2014.Based on different physical backgrounds and different measurements,people propose various of quantum coherence measures,such as l1 norm of coherence and relative entropy of coherence.From the quantum superposition we know any superposition of two quantum states produces a new state,then a question raises that how to describe the change of quantum coherence between the newly obtained quantum state after superposition and the states before superposition.2016,Liu et al.discuss the relationship between the coherence of the states before and after superposition.2017,Yue et al.study the relationship between the coherence of superposition state and the coherence of quantum states used for superposition in high-dimensional system using three different measures.In this paper,using two quantum coherence measures,we study the quantum coherence of the new quantum state which is the superposition of other quantum states.This paper is mainly divided into two parts:Firstly,with l1 norm of coherence,by using the properties of quantum superposition states and l1 norm coherence,we give the upper bounds of the quantum coherence of the quantum states which is superposed by two quantum states in qubit system.Based on these,using mathematical processing methods such as inequality scaling,we give the upper and lower bounds of the quantum coherence of a new quantum state which is superposed with three quantum states in high dimension.Extraordinary,we give the relationship between the coherence of a superposition of n states in terms of the coherence of the n states constituting the superposition.After that,using relative entropy of coherence,by constructing bipartite states and incoherent projection operators,we give the upper and lower bounds for the coherence of the superposition state and that of three orthogonal superposed states before superposition in high dimension.