In general, the number of parameters needed to describe the quantum mechanical state of a system consisting of N subsystems is increasing exponentially with N . For instance, for an N - qubit system, 2 N − − 2 real parameters are needed to describe the state vector of a pure state, or 2 2 N − − 1 real parameters are needed to describe the density matrix of a mixed state. Quantum state tomography is a method to determine all these parameters from a series of measurements on many independent and identically prepared systems. Thus, in the case of full quantum state tomography, the number of measurements needed scales exponentially with the number of particles or qubits.