Entanglement Detection Through State-independent Bound Of Uncertainty Relations

With the rapid development of quantum information theory,entanglement can be regarded as a kind of resource for tasks including,quantum teleportation or quantum computation come true.Many methods for entanglement detection have been proposed,for example,PPT criterion and Bell inequalities.However,there still exists some entangled states not detectable by these means.In this thesis,a possible way of solving this problem is proposed.Uncertainty relations,as a basic property in quantum mechanics,have been widely studied in recently years.However,the standard inequality demonstrating an uncertainty relation between two operators is state-dependent.Here a state-independent bound for uncertainty relation is proposed and we compare it with some optimal bound,showing a better performance.Furthermore,our bound of uncertainty relations can be used for more than three operators.Our bound can be seen as a nonlinear witness for detecting entangled states.In traditional experiments,we measure three orthogonal observables(?x,?y,?z)to verify whether the state is entangled.Our results show that four nonorthogonal may have a better performance.Besides,this bound is also very useful in EPR-steering.