Manuscript Hawk05-B@1 · Hawk05-B.tex · section · f2e5d4f5

A nontrivial conserving realization

One coherent emission history with a Haar hypothesis › A nontrivial conserving realization · lines 478–498

Hawk05-B@1#eq:H0

For each memory cell $M_{j}$ and radiation cell $R_{j}$ , use

H_{M_{j}} = C ∣ \emptyset ⟩ \oplus C^{s}, H_{R_{j}} = C ∣ \emptyset ⟩ \oplus C^{s} .

The preparation occupies all memory cells with the internal state $J ∣ ψ ⟩$ and leaves every radiation cell vacant.

Let $P_{X}$ project onto the occupied sector of cell $X$ . For an energy gap $ω > 0$ , declare

H_{0} = ω j = 1 \sum^{N} (P_{M_{j}} + P_{R_{j}}) .

Extend $U$ to act on the all-occupied memory sector and to be identity elsewhere. Emit cell $j$ by the full SWAP between $M_{j}$ and $R_{j}$ .

Displayed formulas in this passage

Hawk05-B@1#eq:H0 · line 491
$H_{0} = ω j = 1 \sum^{N} (P_{M_{j}} + P_{R_{j}}) .$
unlabeled · line 481
$H_{M_{j}} = C ∣ \emptyset ⟩ \oplus C^{s}, H_{R_{j}} = C ∣ \emptyset ⟩ \oplus C^{s} .$