Manuscript En06-B@1 · En06-B.tex · section · ee886ae8

A product-preserving comparison, not arbitrary compression

Exact instrument and observable refinement › A product-preserving comparison, not arbitrary compression · lines 1764–1789

En06-B@1#eq:iota, En06-B@1#eq:comparisonmaps

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At scale $n$ , use the finite unitary dilation realization with all its reserved factors. The initial physical Hilbert space can be tensor-factor identified as

H_{n}^{phys} ≅ H_{0} \otimes H_{n}^{blank} .

Let $P_{n}$ be this tensor-factor relabelling unitary and define

ι_{n} (A) = P_{n} (A \otimes I_{blank}) P_{n}^{†}, A \in B (H_{0}) .

Set

B_{n}^{log} = ι_{n} (B (H_{0})), j_{n} = ι_{n}^{- 1} .

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unlabeled · line 1769
$H_{n}^{phys} ≅ H_{0} \otimes H_{n}^{blank} .$
En06-B@1#eq:iota · line 1774
$ι_{n} (A) = P_{n} (A \otimes I_{blank}) P_{n}^{†}, A \in B (H_{0}) .$
En06-B@1#eq:comparisonmaps · line 1782
$B_{n}^{log} = ι_{n} (B (H_{0})), j_{n} = ι_{n}^{- 1} .$

A product-preserving comparison, not arbitrary compression

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