I'm having trouble unifying these two ideas. When I read examples using, say, qiskit, it's typical to measure a qubit, so that to find the probability of measuring a state $|\psi \rangle$ in the state $|x\rangle$ is $p(|x \rangle) = (\langle x | \psi \rangle)^2$.

But when I read quantum computing textbooks, they usually refer to some observable that is getting measured. So what is the operator that gets measured when we "measure a qubit"? Is it the identity operator or something?


1 Answer 1


"Measure qubit $q$" = "Measure the $Z_q$ operator"

More generally, "measure the operator $P$" can be operationalized as "apply a sequence operations which sends $P \rightarrow Z_q$ then measure qubit $q$ then undo the operations to restore $Z_q \rightarrow P$.

  • $\begingroup$ What exactly is the $Z_q$ operator? The Pauli $Z$ matrix? $\endgroup$
    – theQman
    Aug 17, 2022 at 18:07
  • $\begingroup$ Exactly, measuring a qubit implicitly means measuring the Pauli-$Z$ observable on the $q$th qubit. This is because $Z$ is already diagonal in the computational basis. $\endgroup$
    – Cody Wang
    Aug 17, 2022 at 19:10

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