Quantum Correlation Of Two Qubits And Its Application In The Quantum Stackelberg Duopoly Game

In this thesis, we study quantum correlation dynamics of two qubits in two independent reservoirs and its application to the quantum Stackelberg duopoly game. We use quantum discord to quantify the quantumness of correlations be-tween two partitions in a composite state proposed by Olliver and Zurek. We study two aspects of quantum correlations between two partitions. On the one hand, we investigate dynamics of quantum discord for two initially-correlated qubits in two independent reservoirs at finite temperature. On the other hand, we investigate how to apply pure quantum discord to the quantum Stackelberg duopoly game. Below are the main results obtained in this thesis.We investigate quantum discord dynamics of two qubits in two independent reservoirs. We obtain the analytical expression of quantum discord dynamics evo-lution for two qubits coupled to independent reservoirs, each in a Ohmic environ-ment under the influence of dephasing interaction when the two qubits are initially prepared in X-type quantum states. It is indicated that the quantum discord dis-plays the sudden-transition phenomenon from a constant regime to a decaying regime in the dynamic evolution under certain conditions. In the quantum discord constant regime, the constant quantum discord can be preserved despite of the existence of decoherence in the system. We focus on discussing how to enhance the preservation duration in order to improve performance in some computational tasks. We show that it is possible to enhance the preservation duration by properly choosing initial state parameters of two qubits, qubit-bath coupling and cut-off fre-quency of the reservoir. In the case of two zero-temperature reservoirs, we have shown that the preservation duration increases with the decrease of the initial-state parameter or/and the decrease of the qubit-bath coupling. Moreover, for a set of given parameters, we have studied the quantum discord dynamics for two qubits in two independent reservoirs at finite temperature. In the case of two nonzero equal-temperature reservoirs, we have found that the decrease of the bath temperature can prolong the preservation duration of the initial quantum discord and slows the quantum discord decay rate. In the case of two unequal-temperature reser-voirs, we have revealed a temperature-difference effect:the larger the temperature difference parameter, the longer the preservation duration.Quantum entanglement is a distinctive feature of quantum correlations, but can't capture all of the nonclassical correlations. We study the influences of un-entangled states with nonzero discordon quantum Stackelberg duopoly game. We obtain a geometric measure of the quantum discord of separable mixed states, and primarily study the influences of quantum discord on the moves of firms A and B at the subgame perfect Nash equilibrium point for the quantum Stackelberg duopoly game and the profits of two players. It is found that there exists a'critical points' of Quantum Stackelberg duopoly game. At the'critical points'the two players (firms A and B) have the same moves and payoffs. We find that the quantum Stackelberg duopoly game can change from the first-mover advantage game into the follower-mover advantage game when the parameter of the state varies from the left-hand-side regime of the'critical points' to the right-hand-side regime, that is to say, the follower firm B becomes better off and the leader firm A becomes worse off. However, the Quantum Stackelberg duopoly game can change from the follower-mover advantage game into the first-mover advantage game when the discord of the state varies from the left-hand-side regime of the 'critical points' to the right-hand-side regime, i.e. the leader firm A becomes better off and the follower firm B becomes worse off. Hence, quantum discord can potentially be a particularly useful element for the'leader firm A'in this regime.