Estimating a Quantum State of a Quantum Mechanical System

A method includes performing quantum state tomography from the statistics of a collection of measurements, each of which has only two possible outcomes and has the feature of being a measurement of a single qubit. By carefully choosing the measurements it becomes possible to infer the state of a quantum system from the statistics. Moreover, the function which computes the state from the measurement statistics can be computed efficiently in the dimension of the underlying system. Reconstructing the quantum state is performed in accordance with the following expression: [..] where d is the dimension of the quantum mechanical system, rho is the state of the quantum mechanical system, Id denotes the identity operator, P_i is one of the plurality of measurement projectors, and p_i is the probability for the measurement projector P_i.