Browsing by Subject "quantum tomography"

The measurement of quantum states has been a widely studied problem ever since the discovery of quantum mechanics. In general, we can only measure a quantum state once as the measurement itself alters the state and, consequently, we lose information about the original state of the system in the process. Furthermore, this single measurement cannot uncover every detail about the system's state and thus, we get only a limited description of the system. However, there are physical processes, e.g., a quantum circuit, which can be expected to create the same state over and over again. This allows us to measure multiple identical copies of the same system in order to gain a fuller characterization of the state. This process of diagnosing a quantum state through measurements is known as quantum state tomography. However, even if we are able to create identical copies of the same system, it is often preferable to keep the number of needed copies as low as possible. In this thesis, we will propose a method of optimising the measurements in this regard. The full description of the state requires determining multiple different observables of the system. These observables can be measured from the same copy of the system only if they commute with each other. As the commutation relation is not transitive, it is often quite complicated to find the best way to match the observables with each other according to these commutation relations. This can be quite handily illustrated with graphs. Moreover, the best way to divide the observables into commuting sets can then be reduced to a well-known graph theoretical problem called graph colouring. Measuring the observables with acceptable accuracy also requires measuring each observable multiple times. This information can also be included in the graph colouring approach by using a generalisation called multicolouring. Our results show that this multicolouring approach can offer significant improvements in the number of needed copies when compared to some other known methods.