Manuscript Hawk02-C@2 · Hawk02-C.tex · section · bb332d66

Label coherence versus packet coherence

Access controls, shared reservoirs, and records › Label coherence versus packet coherence · lines 1946–1976

The decoder uses coherent internal-label access in a known collected mode. It does not read the unknown logical basis or postselect.

Pinching the collected field into vacuum and packet sectors preserves the label code:

r_{N} Tr (X) ∣ a_{0} ⟩ ⟨ a_{0} ∣ + n = 0 \sum^{N - 1} ∣ b_{n} (T) ∣^{2} J_{n} X J_{n}^{†}, J_{n} ∣ a ⟩ = ∣ ϕ_{n}, a ⟩ .

A decoder compressing each sector separately and replacing the complement by $I_{C} / d$ gives

p_{N} id + r_{N} T_{I / d} .

The Bell lower bound proves the same optimum $c_{d} r_{N}$ . Individual packet weights need not be known.

A physical measurement environment is an additional complete output. Its residual is not silently identified with the premeasurement residual.

Destructive label-blind photon counting with all logical carriers discarded leaves a constant record channel: its probabilities depend on $q$ and $∣ b_{n} ∣^{2}$ , not on the input except through its trace. Its optimal recovery error is $c_{d}$ .

Displayed formulas in this passage

unlabeled · line 1954
$r_{N} Tr (X) ∣ a_{0} ⟩ ⟨ a_{0} ∣ + n = 0 \sum^{N - 1} ∣ b_{n} (T) ∣^{2} J_{n} X J_{n}^{†}, J_{n} ∣ a ⟩ = ∣ ϕ_{n}, a ⟩ .$
unlabeled · line 1961
$p_{N} id + r_{N} T_{I / d} .$