Quantum measurements on finite dimensional systems: relabeling and mixing

Erkka Haapasalo, Teiko Heinosaari, Juha-Pekka Pellonpää

Published 2011-04-26, updated 2011-07-14Version 2

Concentrating on finite dimensional systems, we show that one can limit to extremal rank-1 POVMs if two simple procedures of mixing and relabeling are permitted. We demonstrate that any finite outcome POVM can be obtained from extremal rank-1 POVMs with these two procedures. In particular, extremal POVMs with higher rank are just relabelings of extremal rank-1 POVMs and their structure is therefore clarified.