feat(CPTPMap): close 6 sorries around piProd#1067
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dennj wants to merge 1 commit intoleanprover-community:masterfrom
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feat(CPTPMap): close 6 sorries around piProd#1067dennj wants to merge 1 commit intoleanprover-community:masterfrom
dennj wants to merge 1 commit intoleanprover-community:masterfrom
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MatrixMap: - exists_kraus: prove via explicit Kraus decomposition over ((B × A) × A) × B (now requires [StarRing R] [Fintype B]). - Basis.piTensorProduct: drop the local opaque stub and use Mathlib's PiTensorProduct.Basis. - Add choi_matrix_piProd characterising the Choi matrix of piProd. Unbundled: - Add IsTracePreserving.piProd. - Discharge IsCompletelyPositive.piProd via choi_matrix_piProd and Matrix.PosSemidef.piProd. CPTP: - Fill CPTPMap.piProd.TP using IsTracePreserving.piProd (needs maxRecDepth 1000). - fin_1_piProd: replace the sorry-in-type statement with the real equality using ofEquiv (Equiv.funUnique (Fin 1) _) and prove it.
jstoobysmith
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May 4, 2026
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Two comments - though one is really just a comment, the other a question.
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| /-- Finite Pi-type tensor product of MatrixMaps. Defined as `PiTensorProduct.tprod` of the | ||
| underlying Linear maps. Notation `⨂ₜₘ[R] i, f i`, eventually. -/ | ||
| noncomputable def piProd (Λi : ∀ i, MatrixMap (dI i) (dO i) R) : MatrixMap (∀i, dI i) (∀i, dO i) R := |
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Is this definition equivalent to the existing one? What is the reason for the change?
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At some point, I think these CPTP files should be broken up. Maybe we should add a TODO item for this at some point.
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MatrixMap:
Unbundled:
CPTP: