Mixed Quantum State

quantum-computing

Definition

Mixed Quantum State

A mixed quantum state is a quantum state that is a convex combination of at least two distinct pure quantum states:

$$\rho =\sum _i{p}_i|{\psi }_i⟩⟨{\psi }_i|,p_i\ge 0,\sum _i{p}_i=1,$$

where the $|{\psi }_i⟩$ are normalised vectors in a complex Hilbert space $\mathcal{H}$ and not all are equal up to global phase.

A state that is not mixed is a pure quantum state.