I was reading the paper; https://arxiv.org/abs/2002.00055 and going through some of the formulas below and I am a bit stuck between (1) and (2).

How the equation (1) turns into (2) is not clear to me.. Any point or help would be appreciated.

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1 Answer 1


Let the output state (last line of equation 1) be $\sigma$. You're going to measure using projectors (corresponding to a standard basis measurement on the first qubit) $$ P_+=|0\rangle\langle 0|\otimes I, \qquad P_-=|1\rangle\langle 1|\otimes I $$ and you want to know the probability of getting the two outcomes $y=\pm$ for a fixed value of $\theta$, so you could write this as $$ p(y|\theta)=\text{Tr}(P_y\sigma). $$

  • $\begingroup$ Thank you, Are you assuming $ + $ is $|0\rangle $ and $ - $ is $|1\rangle $ and not the superposition of 0 and 1 states? $\endgroup$ Commented Aug 18, 2021 at 15:36
  • $\begingroup$ I'm not assuming. They say "if we interpret the 0/1 outcomes of the measurement as +/- respectively" $\endgroup$
    – DaftWullie
    Commented Aug 18, 2021 at 16:02
  • $\begingroup$ @ Daftwullie, Sorry I missed that part ! :) $\endgroup$ Commented Aug 18, 2021 at 16:04

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