Geometric Discord And Quantum Speed Limit

The quantum information theory is a cross-discipline developed in recent decade. It involves quantum theory, information theory, and many other disciplines. The quantum correlation is attracted much attention since it is an important recourse in quantum information theory. To describe the quantum correlation clearly, the quantum discord and the geometric discord are introduced except the quantum entanglement. In quantum information processing using quantum correlation, to study the evolution time of quantum states, the quantum speed limit time is introduced. In this paper, the geometric discord with arbitrary Bloch vectors and the quantum speed limit time for multiqubit open systems are analyzed. The theoretical results may provide some bases for quantum information processing.In the study of quantum information, it became necessary to develop a sufficient measure of quantum correlation after scientists found that quantum entanglement cannot depict all quantum correlations. Recently, quantum discord was paid a lot of attentions because it is an important measure of quantum correlations. It has many interesting features such as reasonability and robustness. The calculation of quantum discord is not so easy due to its definition. It is difficult to obtain an analytical expression for general two-qubit states. The algorithm for numerical calculation of quantum discord needs a lot of time and recourses. Thus, based on quantum discord, a new measure of quantum correlations called geometric discord is introduced. It not only can describe the properties of quantum discord, but also can reduce the difficulties of calculations. In this paper, based on these properties, the geometric discord for general non-X states with arbitrary directions of Bloch vector is analyzed. From the level surfaces, the effects of the directions of Bloch vector on the geometric discord are studied. Meanwhile, the dynamical properties of geometric discord are investigated when quantum states are in certain damping channels. It is shown that the level surfaces of constant geometric discord are formed by three intersecting open tubes along three orthogonal directions. When Bloch vectors increase, the tubes along one or two directions shrink towards the center and may totally disappear or the open tubes may become closed ones when the Bloch vectors reach a critical value. In generalized amplitude damping channel, the evolution of geometric discord shows double sudden changes when some parameter is increased. In the phase damping channel, the freezing phenomenon of geometric discord also exists.The quantum speed limit(QSL) time comes out following the study of quantum information theory. It studies how fast the time for a quantum system evolving from an initial state to a target state can reach. It is quite useful for quantum computation. In recent years, some new processes of this study have received. When the study of closed system is extended to open system, some interesting results appear. However, former researches mainly focused on single qubit systems, it missed the connection between QSL time and quantum correlation which is an important recourse of quantum information theory. Therefore, in this paper, the quantum speed limit time is investigated when single qubit system is extended to multiqubit open systems. It is shown that the memory(non-Markovian) effect of environment plays an essential role in shortening the QSL time. For certain class of states, the memory effect still acts as the indispensable requirement for cutting the QSL time down, while for another class of states, this takes place even when the environment is of no memory. In particular, when the initial state is in certain product state, there exists a sudden transition from no capacity for potential speedup to potential speedup in memoryless environment. In addition, we also display an evidence for the subtle connection between QSL time and quantum correlation that weak quantum correlation may shorten QSL time even better.