Manuscript Em05-A@1 · Em05-A-v1.tex · remark · 9cac0def

Remark: Fermionic signs and logical parity

The complete signed extraction channel › Occupation ordering and the declared isometry · lines 328–342

The minus sign in (eq:Vone) is the bath-first CAR sign. For residual creators $e_{1}^{†}, e_{2}^{†}$ and bath creators $b_{1}^{†}, b_{2}^{†}$ , expand

(t e_{1}^{†} + η b_{1}^{†}) (t e_{2}^{†} + η b_{2}^{†}) ∣ vac ⟩ .

Moving bath creators before residual creators gives precisely (eq:Vone). Both logical basis vectors have even total fermionic parity. The reference $Q$ is an abstract logical register, not an additional occupation mode. All partial traces use the specified occupation representation.

Displayed formulas in this passage

unlabeled · line 332
$(t e_{1}^{†} + η b_{1}^{†}) (t e_{2}^{†} + η b_{2}^{†}) ∣ vac ⟩ .$

Nearby in this section

section: Occupation ordering and the declared isometry
definition: Definition: Phase-corrected signed extractor
remark: Remark: Relation to a complex transfer amplitude