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

@article{Caves2004GleasonTypeDO,
  title={Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements},
  author={Carlton M. Caves and Christopher A. Fuchs and Kiran K. Manne and Joseph M. Renes},
  journal={Foundations of Physics},
  year={2004},
  volume={34},
  pages={193-209}
}
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… 
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