The Studies On Dynamic Behavior Of Quantum Temporary Steering

Quantum nonlocal correlations,such as quantum entanglement,quantum steering,and Bell nonlocality,play crucial roles in many tasks of quantum communication and quantum computing.However,quantum systems inevitably interact with the external environment,leading to rapid decay of nonlocal correlations,known as decoherence.Therefore,studying the influence of noise and environmental types on the dynamics of quantum correlations in quantum systems,especially in the presence of non-Markovian memory effects,is of paramount importance.In recent years,quantum entanglement and Bell nonlocality have been extensively studied,but research on quantum steering,which lies between the two,is still in its infancy,with many open questions that need to be addressed,especially its dynamics in open systems.Meanwhile,Leggett and Garg proposed a Bell inequality in the time domain,known as the LG inequality.Based on the LG inequality,Chen et al.introduced the concept of temporal steering(TS)as a form of nonlocal correlation in the time domain.Furthermore,recent research has shown that the non-equilibrium features of the environment play important roles in decoherence,quantum speed limits,and Fisher information.From this perspective,this paper focuses on studying the dynamics of TS in two different environmentsFirstly,We explore quantum temporal steering,measured by temporal steering robustness,in a quantum channel described by a qubit coupling to an extended anisotropic XY spin chain associated with non-trivial topological characterization.When the environment channel undergoes a topological quantum phase transition(TQPT)under magnetic field driving,we found that temporal steering robustness is significantly reduced and is also suppressed with the increase of the system size L.At the same time,by calculating the temporal steering robustness power,we can obtain the phase diagram of the environment channel,which is extremely similar to the phase diagram obtained by the topological quantity(i.e.,winding number).In addition,we also analyzed the behavior of the environment channel driven by other parameters(anisotropy of nearest-neighbor interaction,threesite interactions,anisotropy of three-site interactions).Secondly,We investigate the quantum temporal steering(TS),measured by temporal steering robustness,of a two-level system coupling to a nonequilibrium environment,for the weak and the strong coupling regime.We discussed in detail the influence of different environmental parameters(non-equilibrium parameters,memory decay rate,etc.)on the TS dynamics.Numerical results show that in the weak coupling state,when the non-equilibrium parameter is the same,the decay rate of TS will decrease as the memory decay rate increases.At the same time,we also found that only when the memory decay rate is equal to the environment correlation time,periodic decay and recovery will occur,and the decay rate will become faster as the memory decay rate increases.Moreover,at a larger memory decay rate,the decay will become monotonic,which means that as the memory decay rate increases,the system’s evolution will change from non-Markovian to Markovian.In addition,we also analyzed in detail the influence of different environmental parameters on the TS dynamics in the strong coupling state.