Multipartite EPR Steering And Monogamy Relations Of Dynamic Casimir Photons In Coupled Superconducting Waveguides

The dynamic Casimir effect(DCE)was first predicted theoretically by G.T.Moore in 1970,The phenomenon of photon pairs produced by the fluctuation of vacuum is called dynamic Casimir effect.After the theory was proposed,scientists began to try to get real experimental phenomena to verify the theory.The dynamic Casimir effect was first observed in 2011 by willson et al.in an experimental superconducting circuit with tunable coplanar transmission lines of electrical length.As a pioneering quantum effect,it fills resources for the research and development of quantum technology,and also provides a theoretical basis for quantum computing and the preparation of quantum devices.The photon pairs generated in the dynamic Casimir effect show the properties of quantum correlation such as quantum non-locality,quantum EPR steering and quantum entanglement.The quantum EPR steering shows asymmetry,which is different from other quantum correlation properties,so it has a certain research value.A and B are two independent systems.When the state of A is measured,the state of B can be affected non-locally,which is called A steering B.The correlation strength of EPR steering is higher than that of Bell nonlocality and lower than that of quantum entanglement.Two independent systems cannot simultaneously steering a third system.This property is called Monogamy relations.In this paper,we study the EPR steering of dynamic Casimir photon multibody entangled states in four intercoupled superconductive waveguide chains and their corresponding Monogamy relations.The interaction of multiphoton pairs in four coupled superconducting waveguide systems is investigated by multibody EPR guidance with different modes.Based on the witness of EPR steering in the Gaussian continuous variable system,the witness of EPR steering in four coupled superconducting waveguide systems with different modes is deduced.By introducing the concept of steering witness,the influence of temperature ratio,amplitude ratio and coupling coefficient ratio on the occurrence or disappearance speed of EPR steering in different modes can be directly observed.In addition,the EPR steering of different modes in four coupled superconductive waveguide systems presents Monogamy relations from type Ⅰ to type Ⅳ.Then by changing the virtual-real condition and positive and negative condition of the coupling coefficient,the rotation of type Ⅰ monogamy,the exchange and rotation of type Ⅱmonogamy,and the presentation of type Ⅲ and type Ⅳ monogamy characteristics can be realized.