Purity (quantum mechanics)

In quantum mechanics, and especially quantum information theory, the purity of a normalized quantum state is a scalar defined as $${\displaystyle \gamma \,\equiv \,\operatorname {tr} (\rho ^{2})}$$ where ${\displaystyle \rho \,}$ is the density matrix of the state and ${\displaystyle \operatorname {tr} }$ is the trace operation. The purity defines a measure on quantum states, giving information on how much a state is mixed.