Determining a Quantum State by Means of a Single Apparatus

The unknown state ρ̂ of a quantum system S is determined by letting it interact with an auxiliary system A, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix ρ̂ and the probabilities of the occurrence of the eigenvalues of a single and factorized observable of S+A, so that ρ̂ can be determined by repeated measurements using a single apparatus. If S and A are spins, it suffices to measure simultaneously their z components after a controlled interaction. The most robust setups are determined in this case for an initially pure or a completely disordered state of A. They involve an Ising or anisotropic Heisenberg coupling and an external field.