Manuscript Hawk04-B@2 · Hawk04-B.tex · proposition · ba3b0713

Proposition: Access-preserving qubit encoding

Finite proxies and access-preserving qubit dictionaries › Separate finite output dictionaries · lines 1555–1582 · proof included or linked

Hawk04-B@2#prop:qubit-encoding

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There are separate basis isometries

E_{R} : R \to (C^{2})^{\otimes k_{R}}, E_{B} : B \to (C^{2})^{\otimes k_{B}},

where

k_{R} = ⌈ lo g_{2} D_{R} ⌉, k_{B} = ⌈ lo g_{2} D_{B} ⌉ .

Their tensor product preserves the output partition, recovery error, and residual leakage. The encoded prepared proxy admits the coherent finite program of Section subsec:coherent-program.

Proof. Choose separate orthonormal basis dictionaries. Lemma lem:dictionaries proves invariance of the two tasks.

The proxy Hamiltonian acts on its invariant finite total-cutoff subspace. Its unitary extends to the finite ambient tensor product and then to the padded qubit space. The preparation isometry has a unitary extension after allocation by Proposition prop:finite-realization.

Displayed formulas in this passage

unlabeled · line 1558
$E_{R} : R \to (C^{2})^{\otimes k_{R}}, E_{B} : B \to (C^{2})^{\otimes k_{B}},$
unlabeled · line 1563
$k_{R} = ⌈ lo g_{2} D_{R} ⌉, k_{B} = ⌈ lo g_{2} D_{B} ⌉ .$

Proposition: Access-preserving qubit encoding

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