Quantum Tomography with Pauli Operators
In experiments it is often required that we determine an unknown quantum state produced by a source. Quantum Tomography accomplishes this through repeated measurements on the state. This process requires 4^n measurements for an n-qubit system. However, if it is known that the state is pure, fewer measurements are required. Many such results already exist, but they either use non-local measurements or they have some chance of failing. Our goal is to obtain the smallest set of Pauli operators which can uniquely determine any pure state among all states. This involves ensuring the complement of the span of the measurements must have two positive and two negative eigenvalues. This is nontrivial since there are few relationships between the eigenvalues of a set of operators and the eigenvalues their real linear combinations. We obtain the lower bound of 30 Paulis necessary for 3-qubit tomography which improves on any known result.