Schwinger effect of quantum steering for Gaussian states in an electric field

Abstract

In the work, we study the quantum steering for a continuous-variable two-mode squeezed vacuum state shared by Alice and Bob, where Bob's mode experiences a Schwinger effect of a constant electric field. We find that the steering between Alice and Bob decreases with the increasing of the electric field, at the same time the steering between Bob and Anti-Bob is generated. The steering from Alice to Bob results in “sudden death” in the decreasing process, while the steering from Bob to Alice can survive forever. In the production of the steering between Bob and Anti-Bob, the steering from Anti-Bob to Bob shows “sudden birth”, while the steering in the opposite direction is asymptotical. More importantly, we find that the “sudden death” and “sudden birth” appear at the same parameter point, where the steering difference reaches the maximum and the steering transforms between one-way and two-way steering. Moreover, we investigate the case of pulsed electric field, and make a comparison with the case of constant electric field.