Study On Quantum Nonlocal Correlation Based On Microwave Manipulation Technology

Quantum nonlocality and quantum correlation are two unique properties of quantum mechanics. As different kinds of quantum resources, they play important roles in quantum information processing. Up to now, quantum nonlocality characterized by Bell inequality and Hardy’s nonlocality without inequality has been experimentally tested with the entanglement of photons, atoms, trapped ions, an atom and a photon, two degrees of freedom of single neutron, superconducting qubits, etc. Quantum correlation is considered as a more fundamental concept than quantum entanglement in quantum mechanics. In recent years, many researchers focus their attentions on this hot research topic. However, in a realistic condition, a quantum system would inevitably interact with its surrounding environments. This leads to decoherence of this system occurs. Thus it is necessary to study the dynamics of quantum correlation under decoherence. In this dissertation, we study how to test bipartite and tripartite quantum nonlocality in a driven cavity (eg. circuit QED system) based on quantum nondemolition measurements (QNDs) and the dynamics of quantum correlation under local decoherence channels. The major results are listed as follows:1. For two two-level atoms (qubits) dispersively coupled to a driven cavity and considering all the statistical quantum correlations between atoms and cavity (i.e., beyond the mean-field approximation), the QND measurement of two two-level atoms can be realized by detecting steady-state transmission spectra of the driven cavity. Specifically, each peak in the transmission spectra marks one of the computational basis states and the relevant height of such a peak corresponds to the superposed probability of computational basis states in the detected states. With this kind of QND measurements, the generated Bell states can be robustly confirmed without conventional quantum state tomography. Further, the nonlocal correlation functions between local classical variables can be determined by QND measurements. In this way, bipartite quantum nonlocality characterized by Bell inequality and ladder-like Hardy’s nonlocality can be efficiently tested.2. As a natural generalization of the test of bipartite quantum nonlocality, based on the QND measurements of three two-level atoms in a driven cavity, we propose an experimentally feasible proposal to test tripartite quantum nonlocality characterized by Mermin inequality and Svetlichny inequality, for three kinds of three-qubit GHZ, W and biseparable states. It can be found that Mermin inequality can be violated for these three kinds of three-qubit states, while Svetlichny inequality can only be violated by GHZ and W states. This implies that only Svetlichny inequality can characterize genuine tripartite quantum nonlocality. Thus, the violation of Svetlichny inequality can be considered as a robust criterion of the existence of genuine tripartite quantum entanglement.3. The dynamics of geometric measure of quantum discord (GMQD) for a class of two-qubit states under local decoherence channels (bit flip, phase flip and bit-phase flip) is investigated. It can be found that four kinds of dynamical behaviors of the GMQD under decoherence channels exist:monotonic decay to zero; existing a sudden change point during the monotonic decay; existing two sudden change points during the monotonic decay; first keeping unchanged in a finite interval and then monotonic decay to zero. Meanwhile, it can be also found that no sudden death of the GMQD occurs. Furthermore, a relevant factorization law concerning the evolution of the GMQD under decoherence channels is established. From this law, once the decoherence channels are given, the lower bound of GMQD can be obtained, without resorting to the initial quantum state itself.4. We investigate the dynamics of classical correlation, quantum correlation quantified by measurement-induced disturbance (MID) and quantum entanglement for a class of two-parameter qubit-qutrit states under local decoherence channels (dephasing, phase flip, bit/trit flip, bit/trit phase flip and depolarizing). It can be seen that, under certain conditions, classical correlation may be keep unchanged or decay monotonically. MID shows three kinds of dynamical behaviors:monotonic decay to zero; monotonic decay to a nonzero steady value (i.e., residual quantum correlation exists); first increasing from zero to a maximal value and then decay to zero in a monotonic way. Different from the sudden death of quantum entanglement, no sudden death of classical and quantum correlations occurs. Taking the cases in noninertial frames as an example, we study the MID and its dynamics for a class of qubit-qutrit states generated by Unruh effect under these five kinds of local decoherence channels. It can be found that the MID decreases as the acceleration parameter increases. The MID under local decoherence channels can monotonically decay to zero or a nonzero steady value. For the same decoherence parameter, the MID decreases as the acceleration parameter increases.