Quantum measurements on finite dimensional systems: relabeling and mixing



: Haapasalo E, Heinosaari T, Pellonpaa JP

Publisher: SPRINGER

: 2012

: Quantum Information Processing

: QUANTUM INFORMATION PROCESSING

: QUANTUM INF PROCESS

: 6

: 11

: 6

: 1751

: 1763

: 13

: 1570-0755

DOI: https://doi.org/10.1007/s11128-011-0330-2(external)

: https://research.utu.fi/converis/portal/detail/Publication/2781628(external)


Quantum measurements are mathematically described by positive operator valued measures (POVMs). 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.

Last updated on 2024-26-11 at 22:59