Manuscript Hawk01-B@1 · Hawk01-B.tex · section · cfa976f1

Complete occupation cutoffs

Regulators, implementation errors, and certificates › Complete occupation cutoffs · lines 1876–1890

Hawk01-B@1#eq:cutoff

For a finite collection of bosonic modes, let $P_{L}$ project onto total occupation at most $L$ , and define the trace-preserving overflow regulator

R_{L} (ρ) = P_{L} ρ P_{L} + Tr ((I - P_{L}) ρ) ∣ ⊥ ⟩ ⟨ ⊥ ∣ .

With an untouched reference, the overflow branch retains its corresponding reference reduction.

Displayed formulas in this passage

Hawk01-B@1#eq:cutoff · line 1881
$R_{L} (ρ) = P_{L} ρ P_{L} + Tr ((I - P_{L}) ρ) ∣ ⊥ ⟩ ⟨ ⊥ ∣ .$