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Glossary

Quantum glossary

Phase

Also: relative phase, global phase

The angle of a complex amplitude; relative phases between outcomes decide how they interfere.

A global phase on the whole state is unobservable. A relative phase is invisible to a direct measurement but changes everything once the paths are recombined — the “invisible sign” behind most algorithms.

(|0⟩ + e^{iφ}|1⟩)/√2

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Related terms

  • Interference — Amplitudes for the same outcome adding up (constructive) or cancelling (destructive).
  • Amplitude — The complex number attached to each possible outcome of a quantum state; its squared magnitude is that outcome’s probability.
  • Phase kickback — When a controlled operation acts on a target in an eigenstate, the eigenvalue’s phase appears on the control qubit instead.