Distribution Of Coherence For Multipartite Quantum States

As quantum coherence plays an important role in many fields,the quantification of quantum co-herence becomes very necessary.In 2014,after Baumgratz,Cramer and Plenio proposed a set of basic properties that should be satisfied by measuring quantum coherence,the quantification of coherence has entered a rapid development.This paper mainly studies the distribution of coherence for multipartite quantum states,and explores the trade-off relationship of coherence between multipartite quantum states and their subsystems.The former researchs have studied the trade-off relationship between two-qubit states and their subsystems,but there is no clear trade-off relationship between three-qubit states and their subsystems.Based on the above situation,the qubit state is used as the research object in this paper,this paper adopt the measurement method of l1-norm of quantum coherence,which is more convenient to calculate.The trade-off relationship of coherence between the three-qubit states and their two subsystems is presented,and it was generalized to the coherence for multpartite qubit states.The general formulas for the trade-off relationship of multipartite qubit states or high-dimensional quantum states and any of their subsystems are given.The relationship between quantum coherence and quantum entanglement has always been a concern of researchers.It is found that the trade-off relationship between the coherence is restricted by the three tangle of quantum entanglement for pure three-qubit states.So the trade-off relationship of coherence with entanglement is given.Finally,the trade-off relations of coherence for multipartite quantum states by using the Hamming weight and the convex function for two cases 1>?? 0 and ?>1 are presented.