Manuscript Oai212-A@1 · Oai212-A.tex · section · 79323841

Finite-dimensional preparation and entropy errors

Bridge 2: an engineered entanglement-cost membrane › Finite-dimensional preparation and entropy errors · lines 979–990

For $D \geq 1$ , truncate a pair to

∣ ψ_{e, D} ⟩ = \frac{1 - z _{e}}{1 - z _{e} ^{D}} r = 0 \sum^{D - 1} z_{e}^{r /2} ∣ r ⟩_{u} ∣ r ⟩_{v} .

The same Householder construction prepares it by a bounded local gate on two $D$ -dimensional systems.

Displayed formulas in this passage

unlabeled · line 982
$∣ ψ_{e, D} ⟩ = \frac{1 - z _{e}}{1 - z _{e} ^{D}} r = 0 \sum^{D - 1} z_{e}^{r /2} ∣ r ⟩_{u} ∣ r ⟩_{v} .$