In contrast with the classical world,quantum correlations used as physical resource can not be freely shared.For example,if qubit A is maximally entangled with qubit B,then it must be uncorrelated(not even classically)with qubit C.This feature of quantum corretation is termed monogamy.Such a monogamy property is of fundamental importance since it guarantees the security in quantum information communication.Ever since the monogamy relation was quantified for the first time in the seminal paper by Coffman,Kundu,and Wootters(CKW)in 2000 for three qubits,it has been studied intensively in more general settings in the last two decades.All the related results so far are reviewed.Especially,our new definition of monogamy in 2018 and the results based on which we obtained in 2019 are introduced.In addition,the new definition of polygamy relation for measure of quantum correlation and the polygamy relation of the entanglement of assistance are reviewed.Consequently,it is found that our improved definitions of monogamy and polygamy can reveal the distributions of entanglement and the entanglement of assistance more effectively,and that the monogamy of entanglement closely depends on the strict concavity of the reduced function,all the assisted entanglement of entanglement monotones are shown to be polygamous.Our method will shed new light on the studying of the quantum correlations.
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