ブロッホ方程式
s 0 = Tr  ( ρ ^ ) = | c 1 | 2 + | c 2 | 2 = 1 {\displaystyle s_{0}=\operatorname {Tr} ({\hat {\rho }})=|c_{1}|^{2}+|c_{2}|^{2}=1}
s 1 = Tr  ( σ ^ 1 ρ ^ ) = c 1 ∗ c 2 + c 2 ∗ c 1 {\displaystyle s_{1}=\operatorname {Tr} ({\hat {\sigma }}_{1}{\hat {\rho }})=c_{1}^{\,\ast }c_{2}+c_{2}^{\,\ast }c_{1}}
s 2 = Tr  ( σ ^ 2 ρ ^ ) = i ( c 1 c 2 ∗ − c 2 c 1 ∗ ) {\displaystyle s_{2}=\operatorname {Tr} ({\hat {\sigma }}_{2}{\hat {\rho }})=i(c_{1}c_{2}^{\,\ast }-c_{2}c_{1}^{\,\ast })}
s 3 = Tr  ( σ ^ 3 ρ ^ ) = | c 1 | 2 − | c 2 | 2 {\displaystyle s_{3}=\operatorname {Tr} ({\hat {\sigma }}_{3}{\hat {\rho }})=|c_{1}|^{2}-|c_{2}|^{2}}
で与えられる。ここで
s → ( t ) = s 1 e 1 → + s 2 e 2 → + s 2 e 3 → {\displaystyle {\vec {s}}(t)=s_{1}{\vec {e_{1}}}+s_{2}{\vec {e_{2}}}+s_{2}{\vec {e_{3}}}}