Manuscript Hawk02-E@1 · Hawk02-E.tex · section · 4841592b

Finite semidefinite certificates

Complete-residual certificates and decoder certificates › Finite semidefinite certificates · lines 1322–1349

Hawk02-E@1#eq:complement-SDP

The finite complementary Choi operator can be used in the optimization

minimize subject to \frac{1}{2} Tr (X_{+} + X_{-}), J_{n} (C_{t}) - τ_{Q} \otimes σ_{B} = X_{+} - X_{-}, X_{\pm} ⪰ 0, σ_{B} ⪰ 0, Tr σ_{B} = 1.

This is a finite semidefinite program. Its value is the optimized normalized Choi trace distance, not automatically the optimized diamond distance.

Any rigorously feasible tuple supplies an upper certificate. An exploratory floating-point optimum, an unverified positive semidefiniteness test, or a solver residual is not a proof of feasibility.

A direct decoder certificate is also available.

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Hawk02-E@1#eq:complement-SDP · line 1326
$minimize subject to \frac{1}{2} Tr (X_{+} + X_{-}), J_{n} (C_{t}) - τ_{Q} \otimes σ_{B} = X_{+} - X_{-}, X_{\pm} ⪰ 0, σ_{B} ⪰ 0, Tr σ_{B} = 1.$

Finite semidefinite certificates

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