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Determining a quantum state by means of a single apparatus

A. E. Allahverdyan·R. Balian·Th. M. Nieuwenhuizen
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Abstract

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.

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A. E. Allahverdyan, R. Balian, Th. M. Nieuwenhuizen. 2003-11-20. Determining a quantum state by means of a single apparatus. https://doi.org/10.1103/physrevlett.92.120402

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