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FiniteLocalProtocol

Abstract

Every complete finite subtree of local completely positive instruments conserves the trace of every input matrix, including off-diagonal spectator entries. Each node changes only its selected holder and the subsequent tree depends only on its observed outcome.

Theorem 1.1 (complete subtree trace).

Lean statement: D5/S3/Quantum/Recovery/FiniteLocalProtocol.complete_subtree_trace

Proof. Machine-checked in Lean as D5/S3/Quantum/Recovery/FiniteLocalProtocol.complete_subtree_trace (✓ std3). ∎

Source. Repository-derived.

Commentary.

Every complete finite subtree of local completely positive instruments conserves the trace of every input matrix, including off-diagonal spectator entries. Each node changes only its selected holder and the subsequent tree depends only on its observed outcome.

References