Manuscript Hawk06-A@1 · Hawk06-A.tex · definition · c59fe67c

Definition: Decoder prescription

A specified deterministic decoder · lines 822–838

Hawk06-A@1#def:SDP, Hawk06-A@1#eq:SDP

Choose a minimizing solution of the finite semidefinite program

minimize subject to t /2 C_{D} \geq 0, Tr_{L} C_{D} = I_{A^{'}}, Z \geq J_{Δ} (C), Z \geq - J_{Δ} (C), Tr_{L} Z \leq t I_{L^{'}}, t \geq 0.

If several decoder Choi matrices minimize it, choose the unique minimum-Frobenius-norm matrix among those matrices. Denote the resulting CPTP map by $D_{k}^{opt}$ .

Displayed formulas in this passage

Hawk06-A@1#eq:SDP · line 825
$minimize subject to t /2 C_{D} \geq 0, Tr_{L} C_{D} = I_{A^{'}}, Z \geq J_{Δ} (C), Z \geq - J_{Δ} (C), Tr_{L} Z \leq t I_{L^{'}}, t \geq 0.$

Nearby in this section

section: A specified deterministic decoder
theorem: Theorem: Deterministic decoder certificate
section: A specified deterministic decoder