Positive operator-valued measures and densely defined operator-valued frames

Benjamin Robinson, Bill Moran, Doug Cochran

Research output: Contribution to journalArticlepeer-review


In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the purpose of computing measurement probabilities. Frames and their most common generalizations can be seen to give rise to POVMs, but does every reasonable POVM arise from a type of frame? We answer this question using a Radon–Nikodym-type result.

Original languageEnglish (US)
Pages (from-to)265-272
Number of pages8
JournalRocky Mountain Journal of Mathematics
Issue number1
StatePublished - Feb 2021


  • Frames
  • G-frames
  • Operator-valued frames
  • Positive operator-valued measures
  • Radon–Nikodym theorem

ASJC Scopus subject areas

  • General Mathematics


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