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

Exact Haar decoupling and the emission threshold

Exact Haar decoupling and the emission threshold · lines 776–791

For a sharper device-specific certificate, compute

e_{k}^{U} = \frac{1}{2} X_{Q B_{k}}^{U}_{1}, ζ_{k}^{U} = min {1, d e_{k}^{U}} .

These are finite-matrix quantities. One may use the best earlier certificate at a later cut. An ordinary floating-point evaluation without a rigorous norm enclosure is not a certified upper bound.

Displayed formulas in this passage

unlabeled · line 779
$e_{k}^{U} = \frac{1}{2} X_{Q B_{k}}^{U}_{1}, ζ_{k}^{U} = min {1, d e_{k}^{U}} .$

Nearby in this section

section: Exact Haar decoupling and the emission threshold
lemma: Lemma: Two-copy Haar twirl
theorem: Theorem: Exact complementary Hilbert–Schmidt moment
lemma: Lemma: Normalized Choi-to-diamond conversion
section: Exact Haar decoupling and the emission threshold
theorem: Theorem: One unitary, one threshold, all later retained cuts
remark: Remark: What is and is not guaranteed