Manuscript Em05-B@1 · Em05-B-v1.tex · section · 6c050f5b

Normalized Choi and matrix-unit conversions

Referenced certification interfaces › Normalized Choi and matrix-unit conversions · lines 1792–1807

The following conventions prevent a factor-of-two or input-dimension ambiguity in a channel certificate. For input dimension $d$ , define

∣ Φ_{d} ⟩ = \frac{1}{d} i = 1 \sum^{d} ∣ i, i ⟩, J (Φ) = (id_{d} \otimes Φ) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣), E_{ij} = ∣ i ⟩ ⟨ j ∣.

Here $J (Φ)$ is normalized to trace one for a channel.

Displayed formulas in this passage

unlabeled · line 1797
$∣ Φ_{d} ⟩ = \frac{1}{d} i = 1 \sum^{d} ∣ i, i ⟩, J (Φ) = (id_{d} \otimes Φ) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣), E_{ij} = ∣ i ⟩ ⟨ j ∣.$