Quantum measurements on finite dimensional systems: relabeling and mixing

Abstract

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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• Clean Positive Operator Valued Measures
• A two-qubit Bell inequality for which POVM measurements are relevant
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