Research on quantum correlations and Uhlmann phase in two-fermion mixed state system

Abstract Geometric phase, characterized by its unique properties has been an interesting subject since the discovery of Berry phase. A state inevitably becomes a mixed state in the environment. Uhlmann phase can be applied to mixed states and may be the generalization of Berry phase. In this paper, we use a pair of interacting spin-1/2 fermions, where one particle is influenced by an external magnetic field, while the other remains unaffected, to investigate quantum correlations and Uhlmann phase, we define g , p as the ratio of the particle coupling intensity to the magnetic field, and q as the depolarization parameter. Through calculation, we get the specific parameter range q of steering and Bell nonlocality under the depolarized noise channel, q ∈ 0 , 1 − 4 + g 2 4 + 2 g 2 (steering) and q ∈ 0 , 1 − 4 + g 2 4 + 3 g 2 (Bell nonlocality). Moreover, by using Uhlmann phase, we obtain a simple discrimination criterion of the steerability (Bell nonlocality) of the mixed system.