CONVERTING A POSITIVE OPERATOR-VALUED MEASURE TO A DESIGN FOR A MEASURING INSTRUMENT ON THE LABORATORY BENCH

A known positive operator-valued measure (POVM) describing a desired r eceiver of quantum light states is converted into a description of par ts - including a prism, beam splitters and detectors - arranged to mak e a laboratory instrument. The conversion is made in two stages. The f irst is a transparent example of Neumark's theorem, in which a two-dim ensional (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 be have according to their conventional descriptions, the receiver behave s in accord with the given POVM.