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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, +|+\rangle and |-\rangle when measured have the same 50-50 probability of measuring 0|0\rangle or 1|1\rangle (the phase does not impact measurement), but in H+0H|+\rangle → |0\rangle and H1H|-\rangle → |1\rangle, the phase does impact the final measurement.

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