< 1 >
Probability amplitude
In quantum mechanics the probability amplitude is used to indicate the chance that you will find a system in a particular state. It is usually written as
|ψ|^{2}
Explanation
It does not say that a system has a certain state. You must perform a measurement in order to determine a state, and this can be done in several ways, that may produce different results.
Example 1
A qubit can be expressed as a linear combination of the two basic states
|ψ⟩ = α |0⟩ + β |1⟩
where α and β are complex probability amplitudes. The chance that you measure a qubit in the state |0⟩ is |α|^{2} and that you measure state |1⟩ is |β|^{2}, because
|α|^{2} + |β|^{2} = 1
Example 2
A photon can be polarized horizontally or vertically. Until the polarization is measured, the photon is in a superposition of these two states, and we write this as
|ψ⟩ = α |H⟩ + β |V⟩
where α and β are complex probability amplitudes. The chance that you measure a photon in state |H⟩ is |α|^{2} and that you measure state |V⟩ is |β|^{2}, because
|α|^{2} + |β|^{2} = 1