Relative phase

Both columns give 0 and 1 equal chances. The relative sign on the amplitude for 1 has flipped, which a later Hadamard can turn into a certain reading.

The relative phase is the sign, or the angle, between the amplitude for 0 and the amplitude for 1. Two columns with the same chances and a different relative phase are different states. The right gate before the click turns that difference into different chances, and for |+⟩ against |−⟩ a Hadamard makes it a certain reading.

An overall minus sitting on every amplitude is a global phase, which no measurement can see. Decoherence often fades the relative phase before it changes the chances of 0 and 1, and those chances can still be estimated after that fading.

Relative phase

Used in