Fast Quantum State Tomography in the Nitrogen Vacancy Center of Diamond

Quantum state tomography is the procedure for reconstructing unknown quantum states from a series of measurements of different observables. Depending on the physical system, different sets of observables have been used for this procedure. In the case of spin qubits, the most common procedure is to measure the transverse magnetization of the system as a function of time. Here, we present a different scheme that relies on time-independent observables and therefore does not require measurements at different evolution times, thereby greatly reducing the overall measurement time. To recover the full density matrix, we use a set of unitary operations that transform the density operator elements into the directly measurable observable. We demonstrate the performance of this scheme in the electron-nuclear spin system of the nitrogen vacancy center in diamond.