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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Sign up to join this communityI 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.
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 $$ p(y|\theta)=\text{Tr}(P_y\sigma). $$