Determining an n-qubit state by a single apparatus through a pairwise interaction

This paper shows how one can reconstruct an unknown n-qubit state by only a single apparatus. Its core is a redistribution of the information within an extended Hilbert space by coupling the unknown system with an assistant system through only a pairwise interaction, which results in a one-to-one mapping between the unknown density matrix elements and the probabilities of the occurrence of the eigenvalues of a single, factorized observable of the composite system. In such an interaction configuration, which is more feasible in experiments, the quality of the measurement only depends on that of the subsystem consisting a of one-qubit system coupled to a one-qubit assistant. We analyze in detail the performance of this procedure and experimentally implement it for reconstructing an unknown two-qubit state using a four-nuclear-spin system.