Neumark's theorem and quantum inseparability

Abstract

The most efficient way of obtaining information about the state of a quantum system is not always a direct measurement. It is sometimes preferable to extend the original Hilbert space of states into a larger space, and then to perform a quantum measurement in the enlarged space. Such an extension is always possible, by virtue of Neumark's theorem. The physical interpretation usually given to that theorem is the introduction of an auxiliary quantum system, prepared in a standard state, and the execution of a quantum measurement on both systems together. However, this widespread interpretation is unacceptable, because the statistical properties of the supposedly standard auxiliary system are inseparably entangled with those of the original, unknown system. A different method of preparing the auxiliary system is proposed, and shown to be physically acceptable.