Manuscript Oai280-B@1 · Oai280-B.tex · section · 6d92ab75

An exactly solved flagged-erasure benchmark

An exactly solved flagged-erasure benchmark · lines 1880–1906

For the positive access sizes:

m 345 p_{m} (q) q^{3} 4 q^{3} (1 - q) + q^{4} 10 q^{3} (1 - q)^{2} + 5 q^{4} (1 - q) + q^{5}

At $q = 1$ this recovers the ideal access table. At $q = 0$ every channel has optimal error $3/4$ .

The decoded channel is Pauli. Its three oriented failure probabilities are all

p_{j}^{failure} = \frac{1 - p _{m} ( q )}{2},

and its Bell overlap is $F = 1 - \frac{3}{4} (1 - p_{m} (q))$ . These give explicit nonideal laws for (eq:exactpower). They are justified for this erasure model, not transferred to an arbitrary implemented boundary process.

Displayed formulas in this passage

unlabeled · line 1883
$m 345 p_{m} (q) q^{3} 4 q^{3} (1 - q) + q^{4} 10 q^{3} (1 - q)^{2} + 5 q^{4} (1 - q) + q^{5}$
unlabeled · line 1897
$p_{j}^{failure} = \frac{1 - p _{m} ( q )}{2},$

Nearby in this section

section: An exactly solved flagged-erasure benchmark
theorem: Theorem: Exact complete flagged-erasure optimum