Manuscript En01-C@1 · En01-C.tex · section · 00a2161c

Outcome mixing can destroy coherence

Finite packet and finite-window corrections › Outcome mixing can destroy coherence · lines 1246–1263

For $z \in W$ , project the corresponding block into the same two output modes, possibly after a fixed record-conditioned routing map. Write

P_{\pm} (z) = ⟨ u_{\pm}, τ (z) u_{\pm} ⟩, B (z) = P_{+} (z) P_{-} (z) V (z) e^{i α (z)} .

Define

H_{W} = \frac{\int _{W} P _{+} ( z ) P _{-} ( z ) d z}{\int _{W} P _{+} ( z ) d z \int _{W} P _{-} ( z ) d z} .

Cauchy–Schwarz gives $0 \leq H_{W} \leq 1$ .

Displayed formulas in this passage

unlabeled · line 1251
$P_{\pm} (z) = ⟨ u_{\pm}, τ (z) u_{\pm} ⟩, B (z) = P_{+} (z) P_{-} (z) V (z) e^{i α (z)} .$
unlabeled · line 1257
$H_{W} = \frac{\int _{W} P _{+} ( z ) P _{-} ( z ) d z}{\int _{W} P _{+} ( z ) d z \int _{W} P _{-} ( z ) d z} .$