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The usual definition of complete positivity (e.g. Stinespring (1955), or Holevo's Statistical Structure of Quantum Theory) is that a linear map between (sub $C^*$ algebras of) the bounded operators on ...

I suspect this is the obvious result of something in operator algebras, but that's far outside my field. Recall that a projection-valued measure is a map $E$ from a sigma-algebra $\mathcal{F}$ on ...

I was recently made aware (thanks to the answers on Why does Riesz's Representation Theorem apply in quantum mechanics?) that the $C^*$ algebra approach and the Hilbert space approach to quantum ...

One of the basic postulates in the mathematical formalism of quantum mechanics is that the probability of a measurement of an observable $A$ in the state $\psi \in \mathscr{H}$ to return a value in a ...