quantum-computing quantum-mechanics
Definition
Normalised Quantum State
Let
be a complex Hilbert space. A normalised quantum state is a quantum state represented by a vector with unit norm: Equivalently, using bra-ket notation,
Thus a normalised quantum state is a unit vector in the quantum state space.
Why Normalisation Is Required
The Born rule assigns probabilities by squared amplitudes. For a basis expansion
the total probability is
Therefore probabilities sum to