Genuine Einstein-Podolsky-Rosen Steering Of Generalized Three-Qubit States Via Unsharp Measurements

EPR steering is a kind of quantum correlation between quantum entanglement and Bell non-locality,and it is also one of the non-classical characteristics of quantum mechanics.It plays a very important role in quantum information processing tasks,such as quantum key distribution,quantum randomness verification etc.Therefore,it is necessary to study the EPR steering detection of quantum states.Up to now,there have been researched on the EPR steering detection for the two-qubit and three-qubit maximally entangled states,but the researches on the multiple observers of EPR steering detection for generalized three-qubit entangled states are rare.This article aims to explore all possible scenarios of(1→2)(where one wing is untrusted and the other two wings are trusted)and(2→1)(where two wings are untrusted,and one wing is trusted)genuine tripartite EPR steering.The generalized Greenberger-Horne-Zeilinger(GHZ)state and generalized W state are shared between three spatially separated parties,Alice,Bob and Charlie.In both(1→2)and(2→1),we discuss the untrusted party and trusted party performing a sequence of unsharp measurements,respectively.For each scenario,we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality.The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters.Moreover,both the sharpness parameters range and the state parameters range in the scenario of(1→2)steering are larger than those in the scenario of(2→1)steering.For the generalized W states with entanglement parameters between 0 and π/4.In a one-sided device-independent scenario,there are three trusted parties in the sequence or three untrusted parties in the sequence to establish steering with the other two parties.In a two-sided device-independent scenario,there are two trusted parties in the sequence or two untrusted parties in the sequence,respectively,to establish the steering with the other two parties.