Abstract:In 1940 Naimark showed that if a set of quantum observables are positive
semi-definite and sum to the identity then, on a larger space, they have a
joint resolution as commuting projectors. In 1955 Sz.-Nagy showed that any set
of observables could be so resolved, with the resolution respecting all linear
sums. Crucially, both resolutions return the correct Born probabilities for the
original observables. Here, an alternative proof of the Sz.-Nagy result is
given using elementary inner product spaces. A version… Show more
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