Uncertainty principle
Mixed states

The Robertson–Schrödinger uncertainty relation may be generalized in a straightforward way to describe mixed states. σ A 2 σ B 2 ≥ | 1 2 tr (ρ { A, B }) − tr (ρ A) tr (ρ B) | 2 + | 1 2 i tr (ρ) | 2. {\displaystyle \sigma _{A}^{2}\sigma _{B}^{2}\geq \left|{\frac {1}{2}}\operatorname {tr} (\rho \{A,B\})-\operatorname {tr} (\rho A)\operatorname {tr} (\rho B)\right|^{2}+\left|{\frac {1}{2i}}\operatorname {tr} (\rho)\right|^{2}.}
startend:quotation