Converting a positive operator-valued measure to a design for a measuring instrument on the laboratory bench
John M. Myers, Howard E. Brandt · Measurement Science and Technology · 1997
A known positive operator-valued measure (POVM) describing a desired receiver of quantum light states is converted into a description of parts - including a prism, beam splitters and detectors - arranged to make a laboratory instrument. The conversion is made in two stages. The first is a transparent example of Neumark's theorem, in which a two-dimensional (non-projective) POVM is converted into a Hermitian operator on a space of three dimensions. The second uses a known factorization of the Hermitian operator into a product of simpler operators, each a conventional description of an optical component. If the components behave according to their conventional descriptions, the receiver behaves in accord with the given POVM.