2状態系
と展開できる。但し、展開係数は
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 })}