Measuring two Charge Qubits with one Single Electron Transistor

In this thesis, we investigate a proposal for measuring two coupled quantum dot (CQD) charge qubits. The measurement device is a single electron transistor (SET) which con-sists of two quantum point contacts (QPCs) serially connected by a Coulomb island. The two QPCs are capacitively coupled to the two charge qubits. By monitoring the current through the SET, the state of the coupled qubits can be detected. Within an open system approach, a Markoffian master equation of this system is de-rived. By solving the Markoffian master equation, time evolution of the average current flowing through the SET is simulated with different initial two-qubit state. To study the current fluctuations, a technique named full counting statistics (FCS) is used. With this technique, the probability distributions of the number of electrons tunneled through the SET within particular time intervals are calculated. In order to better understand the continuous quantum measurement process, we also calculate three important time scales: the dephasing time, the measurement time, and the mixing time. I I