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The third-order polarization measurement $P_3(t)$ is therefore  \[ P_3(t) = \left(\begin{array}{c}0 & \left(\begin{array}{c}  0 & \\  0 & F\\\end{array}\right) \\  0 \\  F \\  \end{array}\right) \cdot  x(t)\] such that $F \cdot = \avg{\mu \cdot}$, in operator form. $x(t)$ is governed by the time evolution equation