Determining a quantum state by means of a single apparatus
A. E. Allahverdyan, R. Balian, Th. M. Nieuwenhuizen
Abstract
The unknown state 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 and the probabilities of occurrence of the eigenvalues of a single and factorized observable of S+A, so that 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.
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