  The unknown state $\hrho$ 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 $\hrho$ and
the probabilities of occurrence of the eigenvalues of a single and factorized
observable of S+A, so that $\hrho$ 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.
