Journal
QUANTUM INFORMATION PROCESSING
Volume 11, Issue 6, Pages 1751-1763Publisher
SPRINGER
DOI: 10.1007/s11128-011-0330-2
Keywords
Quantum measurement; POVM; Relabeling; Mixing
Funding
- Academy of Finland [138135]
- Emil Aaltonen Foundation
- Academy of Finland (AKA) [138135, 138135] Funding Source: Academy of Finland (AKA)
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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.
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