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A Few Remarks on Milburn Equation

After presenting the infinite operator-sum form solution to the Milburn equation dρ/dt = γ(UρU† – ρ) = γU[ρ,U†], where U = e-iH/ℏγ, and verifying that this equation preserves the three necessary conditions of density operators during time evolution, we prove that the von Neumann entropy increases with time. We also point out that if A and B both obey the Milburn equation, then the product AB obeys (d/dt) (AB) = γU[AB, U†] – (1/γ) (dA/dt) (dB/dt), which violates the Milburn equation, this reflects that a pure state will evolve to a mixture in general.