Clean positive operator valued measures for qubits and similar cases
arXiv:quant-ph/0603117 · doi:10.1088/1751-8113/40/18/009
Abstract
In a recent paper, Buscemi and al. defined a notion of clean positive operator valued measures (POVMs). We here characterize which POVMs are clean in some class that we call quasi-qubit POVMs, namely POVMs whose elements are all rank-one or full-rank. We give an algorithm to check whether a given quasi-qubit POVM satisfies to this condition. We describe explicitely all the POVMs that are clean for the qubit. On the way we give a sufficient condition for a general POVM to be clean.
15 pages, Much of a sequel to quant-ph/0505095 Rewriting of the article deeply improving (I hope) the presentation. Accepted for publication in Journal of Physics A