Manuscript Hawk02-D@1 · Hawk02-D.tex · section · e6e4b72f

Access and the complete residual

The autonomous fermionic source–reservoir model › Access and the complete residual · lines 559–604

For $M \geq 1$ , define the collected one-particle space

r_{M} = span {e_{1}, \dots, e_{M}} \otimes C^{n},

and its complete orthogonal complement

b_{M} = (span {e_{0}} \oplus span {e_{M + 1}, e_{M + 2}, \dots}) \otimes C^{n} .

Fix once and for all the occupation-space factorization

F_{f} (h) ≃ F_{f} (r_{M}) \otimes F_{f} (b_{M}) .

The grading signs are fixed by this ordering; no message-dependent factorization is used.

The accessible output is

R_{M} = F_{f} (r_{M}) .

The complete residual includes

B_{M} = F_{f} (b_{M}) \otimes carrier output.

The carrier factor is fixed vacuum by Proposition prop:loading. All reservoir modes not collected remain in $B_{M}$ .

Access means unrestricted coherent batch access to $R_{M}$ at the observation time. It is not a streaming-memory theorem, a compact local detector construction, or an assertion of bounded decoding complexity.

Displayed formulas in this passage

unlabeled · line 562
$r_{M} = span {e_{1}, \dots, e_{M}} \otimes C^{n},$
unlabeled · line 568
$b_{M} = (span {e_{0}} \oplus span {e_{M + 1}, e_{M + 2}, \dots}) \otimes C^{n} .$
unlabeled · line 579
$F_{f} (h) ≃ F_{f} (r_{M}) \otimes F_{f} (b_{M}) .$
unlabeled · line 588
$R_{M} = F_{f} (r_{M}) .$
unlabeled · line 592
$B_{M} = F_{f} (b_{M}) \otimes carrier output.$