Some non-algebraic forms of $\exp(A+B)$

We present examples where expressions for $\exp (\hat{A} + \hat{B})$ can be derived even though the operators (or superoperators) $\hat{A}$ and $\hat{B}$ do not commute in a manner that leads to known factorizations. We apply our factorization to the case of a Lindblad operator modeling single photon decay and to a binary Glauber-Fock photonic lattice.

Some non-algebraic forms of $\exp (A + B)$

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Some non-algebraic forms of $\exp (A + B)$

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Some non-algebraic forms of exp⁡(A+B)exp(A+B)

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Some non-algebraic forms of exp⁡(A+B)exp(A+B)

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Some non-algebraic forms of $\exp (A + B)$

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Some non-algebraic forms of $\exp (A + B)$

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