Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements

  title={Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements},
  author={C. Caves and C. Fuchs and Kiran K. Manne and J. M. Renes},
  journal={Foundations of Physics},
  • C. Caves, C. Fuchs, +1 author J. M. Renes
  • Published 2004
  • Physics, Mathematics
  • Foundations of Physics
  • We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures (POVMs), as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems (qubits) and even for vector spaces over rational fields—settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original… CONTINUE READING

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