Manuscript Em03-B@2 · Em03-B-v2.tex · theorem · c1a0977d

Theorem: Derived B5 implementation budget

B5: a complete readout apparatus and its errors › Derived quantum and preparation bounds · lines 1683–1713 · proof included or linked

Em03-B@2#thm:readbudget, Em03-B@2#eq:readbudget

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The complete readout channel of Specification spec:readnoise obeys

d_{⋄} (P_{N}^{S}, P_{N}^{S}) \leq δ_{N}^{model} := min {1, r_{F} + (1 - r_{F}) (p_{A} + δ_{D} + δ_{B} + δ_{X} + δ_{R} + δ_{as})} .

Proof. On a ready branch, replace the independent pointer preparation by the all-zero state at cost $p_{A}$ . Telescope the quantum operations using Lemma lem:readcomponents. Then apply Theorem thm:assignment. This gives the ready-branch bound.

The failure branch has the same output alphabet and differs from the ideal channel by half-diamond distance at most one. Convexity therefore costs $r_{F}$ , while the ready budget has weight $1 - r_{F}$ .

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Em03-B@2#eq:readbudget · line 1687
$d_{⋄} (P_{N}^{S}, P_{N}^{S}) \leq δ_{N}^{model} := min {1, r_{F} + (1 - r_{F}) (p_{A} + δ_{D} + δ_{B} + δ_{X} + δ_{R} + δ_{as})} .$

Theorem: Derived B5 implementation budget

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