Nondestructive Estimation of the Eigenvectors of Mixed State

Given n qubits prepared according to the same mixed state ρ, we propose a measuring scheme which approximately yields the eigenvectors of ρ. By performing a sequence of measurements, we can scan the Bloch sphere like radar to search for the eigenvectors. It is shown that this scheme is nondestructive when n is large. This result is based on the quantum typical subspace theory and it actually reveals an interesting mathematical structure of the n-fold Hilbert space.