Nonlocality Of Two Qubits In A Environment

Quantum correlations are a basic resource for realizing quantum information schemes.Quantum discord is a non-classical correlation and is regarded as the key concept in quantum information science.In recent years,the measurement-induced nonlocality(MIN)introduced by Luo and Fu is another kind of quantum correlations,which reveals that there is a kind of nonlocality in composite quantum states,which plays an important role in quantum information theory and technology.Due to the complexity of optimization calculation,it is difficult to obtain analytical formulas for quantum discord and nonlocality in general.In this paper,the dynamics of the measurement-induced nonlocality and geometric discord for two qubits in the environment is investigated.We calculate three kinds of measurement-induced nonlocality and geometric discord by using Monte Carlo simulation and downhill simplex algorithm.In addition,we compare these three kinds of nonlocality and geometric discord respectively.Firstly,we give the theory of quantum information,,which includes the concept of density matrix and reduced density matrix,the definitions of three kinds of measurement-induced nonlocality,and three kinds of geometric discord.Additionally,Monte Carlo simulation and downhill simplex algorithm are introduced,which are two important numerical simulations.Secondly,we use analysis and numerical simulations to study the dynamics of nonlocality and geometric discord for two qubits interacting with an environment under the given initial state and model parameters.The results show that those three measurement-induced nonlocalities have similar behaviors with evolution time,that is,they appear the trend of decreasing and then increasing with time,where the minimum value is a sudden change.Under the same environmental conditions,three geometric discord exhibit similar decay in the dynamical evolution,and they occur minimum and maximum values.However,the minimum values gradually disappear by adjusting the model parameters and the average number of thermal photons.The difference among three disocrds is that the 1-norm geometric discord is approximately linear evolution,while the original 2-norm geometric discord and the geometric discord based on fidelity measurement exhibit non-linearity.There is no asymptotic decay behavior for those measurement-induced nonlocalities,whereas there is for those discords.These properties can motivate one to deeply study quantum correlations theoretically and experimentally,so as to set up a proper measure of quantum correlations and accomplish quantum information tasks.In summary,we study the quantum correlation dynamics of two qubits in an environment.We find that different correlation measures have different dynamic behaviors,and quantum correlation measures can be adjusted by initial states and model parameters.In the future,we shall discuss quantum correlation properties in other systems and their possible applications in quantum information processes.