Turns out the reasoning in supplementary information IV.C is kind of flawed, but the results follow trivially from the definition of expectation and probability

Turns out the reasoning in supplementary information IV.C is kind of flawed, but the results follow trivially from the definition of expectation and probability mass function. Wrote it up here: https://quantumcomputing.stackexchange.com/a/8565/8704 https://quantumcomputing.stackexchange.com/a/8565/8704