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Simplifying transition pathways by adding weights pathways which are the same except where p=0

Open mgiammar opened this issue 3 years ago • 0 comments

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.

mgiammar avatar May 23 '22 17:05 mgiammar