Petrovcic2x

2022-06-23

Show that measuring the observable $|1\u27e9\u27e81|$ is equivalent to measuring the observable Z up to a relabelling of the measurement outcomes.

What does it mean by relabelling of the measurement outcomes and how do I prove it? Could anyone help me?

What does it mean by relabelling of the measurement outcomes and how do I prove it? Could anyone help me?

arhaitategr

Beginner2022-06-24Added 13 answers

Measuring the observable Z means that you collapse to either $|0\u27e9\u27e80|$ or to $|1\u27e9\u27e81|$, this is exactly the same as measuring the observable $|1\u27e9\u27e81|$, in which case you get that outcome or the opposite outcome $1-|1\u27e9\u27e81|=|0\u27e9\u27e80|$.