measured standard basis Born rule norm-squared collapses qubit measuring bit
When a qubit is measured in the standard basis, the result is a classical bit.
The Born rule describes the norm-squared correspondence between amplitudes and probabilities—when measuring a qubit α|0⟩ + β|1⟩, the state collapses to |0⟩ with probability |α|, or to |1⟩ with probability |β|.
Any valid qubit state has coefficients α and β such that |α| + |β| = 1.
As an example, measuring the qubit 1/√2|0⟩ + 1/√2|1⟩ would produce either |0⟩ or |1⟩ with equal probability.
