Manuscript Oai265-B@2 · Oai265-B-v2.tex · section · 94b6f42f

Standard finite-dimensional conversions

Standard finite-dimensional conversions · lines 384–397

The required normalization-sensitive facts are proved locally. They are established tools KlieschRoth,FuchsVanDeGraaf,Watrous.

For input dimension $d$ , define

∣ Φ_{d} ⟩ = \frac{1}{d} i = 0 \sum^{d - 1} ∣ i, i ⟩, P_{d} = ∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣, J_{Φ} = (id_{d} \otimes Φ) (P_{d}) .

For a channel, $J_{Φ}$ has trace one.

Displayed formulas in this passage

unlabeled · line 391
$∣ Φ_{d} ⟩ = \frac{1}{d} i = 0 \sum^{d - 1} ∣ i, i ⟩, P_{d} = ∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣, J_{Φ} = (id_{d} \otimes Φ) (P_{d}) .$