The Importance of Phase in Quantum Mechanics

Although when finally measuring, the phase does not play an impact on the probability of measuring a state, it does play an impact in the quantum circuit before measurement when quantum gates are applied. While an entangled state is going through a quantum circuit, its phase is affected by its interactions with the gates and can lead to different probabilities. For example, and when measured have the same 50–50 probability of measuring or (the phase does not impact measurement), but in and , the phase does impact the final measurement.

The phase stores extra information, which can be extracted through gates like the Hadamard gate.