Decomposition of any quantum measurement into extremals
Gael Sentís, B. Gendra, Stephen D. Bartlett, Andrew C. Doherty · Journal of Physics A Mathematical and Theoretical · 2013
We design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements. We show that if one allows for a classical post-processing step only extremal rank-1 positive operator valued measures are needed. For a measurement with N elements on a d -dimensional space, our algorithm will decompose it into at most ( N − 1) d + 1 extremals, whereas the best previously known upper bound scaled as d 2 . Since the decomposition is not unique, we show how to tailor our algorithm to provide particular types of decompositions that exhibit some desired property.