Manuscript Oai276-A@1 · Oai276-A.tex · section · 215068af

The generalized amplitude-damping convention

Stage 0: freeze the channel, units, and claims › The generalized amplitude-damping convention · lines 258–291

Oai276-A@1#eq:channel, Oai276-A@1#eq:kraus

For $γ, ν \in [0, 1]$ , write $k = 1 - γ$ . The channel is

A_{γ, ν} (1 - p z z p) = (1 - t k z k z t), t = (1 - γ) p + γ ν .

Here $ν$ is the stationary excited-state population, not an unidentified bosonic occupation number.

A Kraus family is

L_{0} L_{2} = 1 - ν diag (1, k), = ν diag (k, 1), L_{1} L_{3} = γ (1 - ν) ∣0 ⟩ ⟨ 1∣, = γ ν ∣1 ⟩ ⟨ 0∣.

Displayed formulas in this passage

Oai276-A@1#eq:channel · line 262
$A_{γ, ν} (1 - p z z p) = (1 - t k z k z t), t = (1 - γ) p + γ ν .$
Oai276-A@1#eq:kraus · line 281
$L_{0} L_{2} = 1 - ν diag (1, k), = ν diag (k, 1), L_{1} L_{3} = γ (1 - ν) ∣0 ⟩ ⟨ 1∣, = γ ν ∣1 ⟩ ⟨ 0∣.$