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Simplifying transition pathways by adding weights pathways which are the same except where p=0
For a list of pathways which include symmetries of p=0, the given transition pathways might only differ by the p=0 transition. In that case, pathways with the same transition (except for the p=0) can have their weights added to create a list of simplified pathways. For example, the following 6 transition pathways could be simplified down to 2 transition pathways
[|-1.0⟩⟨1.0| ⟶ |-1.0⟩⟨-1.0| ⟶ |0.0⟩⟨-1.0|, weight=(1+0j),
|-1.0⟩⟨1.0| ⟶ |-1.0⟩⟨-1.0| ⟶ |1.0⟩⟨0.0|, weight=(1+0j),
|-1.0⟩⟨1.0| ⟶ |0.0⟩⟨0.0| ⟶ |0.0⟩⟨-1.0|, weight=(1+0j),
|-1.0⟩⟨1.0| ⟶ |0.0⟩⟨0.0| ⟶ |1.0⟩⟨0.0|, weight=(1+0j),
|-1.0⟩⟨1.0| ⟶ |1.0⟩⟨1.0| ⟶ |0.0⟩⟨-1.0|, weight=(1+0j),
|-1.0⟩⟨1.0| ⟶ |1.0⟩⟨1.0| ⟶ |1.0⟩⟨0.0|, weight=(1+0j)]
equivalent to
[|-1.0⟩⟨1.0| ⟶ |0.0⟩⟨-1.0|, weight=(1+0j),
|-1.0⟩⟨1.0| ⟶ |1.0⟩⟨0.0|, weight=(1+0j)]
The weights here would sum to 3, but that is because TotalMixing causes all weights to go to 1. More discussion on how to handle certain cases is warranted.