论文标题
由大型随机矩阵建模的公共环境中两个量子位的量子相关性的动力学
The Dynamics of Quantum Correlations of Two Qubits in a Common Environment Modeled by Large Random Matrices
论文作者
论文摘要
本文是我们以前的论文[8]的延续，其中我们研究了两个量子的量子相关性动态，每个量子位嵌入了其自身无序的多连接环境中。我们通过大尺寸的随机矩阵对环境进行建模，从而有可能描述中索环境甚至纳米环境。在本文中，我们还研究了两个量子位的量子相关性的动力学，但嵌入了一个共同的环境中，我们还通过大尺寸的随机矩阵进行建模。我们获得了两个量子位的降低密度矩阵的大尺寸极限。然后，我们使用Bogolyubov-Van Hove（也称为Born-Markov）的类似物对开放系统和统计力学理论的近似。通常，近似并不意味着我们模型中的马尔可夫进化，而是允许对几种广泛使用的量子相关量化器（主要是纠缠的量子）的演变进行足够详细的分析和数值。我们发现，与[8]中研究的独立环境的情况相比，Qubits动力学的许多新模式，并在增强量子进化的增强和多样化中显示动力学（间接，通过环境）相关性的作用。我们的结果（在[9]中宣布）可以看作是磨碎量子的演变某些特性的普遍性的表现，这些量子的普遍性以前在具有宏观波索克环境的两个Qubit模型的各种精确和近似版本中都发现。
This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of large size allowing for a possibility to describe meso- and even nanoenvironments. In this paper we also study the dynamics of quantum correlations of two qubits but embedded into a common environment which we also model by random matrices of large size. We obtain the large size limit of the reduced density matrix of two qubits. We then use an analog of the Bogolyubov-van Hove (also known as the Born-Markov) approximation of the theory of open systems and statistical mechanics. The approximation does not imply in general the Markovian evolution in our model but allows for sufficiently detailed analysis both analytical and numerical of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a number of new patterns of qubits dynamics comparing with the case of independent environments studied in [8] and displaying the role of dynamical (indirect, via the environment) correlations in the enhancing and diversification of qubit evolution. Our results, (announced in [9]), can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution which have been found previously in various exact and approximate versions of two-qubit models with macroscopic bosonic environment.
