Local Quantum Uncertainty In Many-body System

Quantum information science is a new discipline which is produced by the combination of quantum mechanics and classical information science. Quantum information science mainly consists of quantum communication, quantum computing and quantum cryptography, due to quantum superposition, quantum coherence and quantum entanglement, making quantum information science can complete the task that classical information can not complete.In the development of quantum information, we use quantum entanglement to measure the quantum correlation, but with the development of quantum information science, it is found that the non entangled quantum correlations exist in separable states, and it also plays a very important role in quantum information processing.We study the quantum correlations in symmetric multi-qubit systems, and discuss three quantum correlation of a random pair of particles drawn from a symmetric state of N two-level systems, namely local quantum uncertainty, geometric measure of quantum discord and Concurrence. The superposition of Dicke States, generalized GHZ States, Dicke States and even and odd CSSs(coherent spin state) are selected to study their corresponding quantum correlations. We get the trend of change of the corresponding quantum correlations by the change of some parameters, we also make some analysis. At last we get that the local quantum uncertainty can be used to measure the quantum correlations.And then we study the local quantum uncertainty of a mixed-spin Heisenberg XY chain, through comparing the Negativity and local quantum uncertainty, one can get the influence of the external magnetic field B and temperature T on them. In conclusion, we get that the local quantum uncertainty can be used to measure the quantum correlations of the model, and in the high temperature condition, Negativity is 0 but the local quantum uncertainty is not.Finally, we study the quantum correlations of the Ising-XXZ diamond chain structure, and get the density plot of the local quantum uncertainty by the change of temperature T and anisotropic coefficient △, the external magnetic of Ising-spin h and Ising-interaction J1,and the external magnetic of Ising-spin h and temperature T. We also make some analysis for these density plot.