I study Qiskit. When I measure a qubit by including qc.measure(qb,cb) instruction, I measure it in the computational basis. But if I apply the Hadamard gate adding qc.h(qb) before the measurement qc.measure(qb,cb), it is often referred to as measuring in X-basis. In my mind measuring in a different basis should involve some changes in the measurement apparatus, not in the state of the system being measured (as happens in this case). I understand that computationally, applying the Hadamard gate produces the same outcome as the actual measurement in a different basis, but I'm just curious why it is call the 'change of basis'. Is it just some informal naming convention or does it have some hidden meaning?
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Any unitary operator can be understood as a change of basis in which we describe operators in quantum theory.
Specifically, the Hadamard gate is a unitary that sends the basis $\{\vert 0\rangle , \vert 1\rangle\}$ into the basis $\{\vert + \rangle, \vert - \rangle\}$. If you note, we changed the eigenbasis of Z into the eigenbasis of X.
