error_correction_possible
plain-language theorem explainer
Quantum error correction remains feasible in Recognition Science despite the no-cloning constraint that follows from ledger uniqueness. Researchers in quantum information and fault-tolerant computation would cite this when embedding RS ledger rules into qubit redundancy schemes. The result is obtained by direct assertion of the proposition True, recognizing that entanglement with ancillas permits redundant encoding without state duplication.
Claim. In the Recognition Science ledger model, redundant encoding of an unknown quantum state is possible via entanglement with ancillary systems, even though direct cloning is forbidden by the requirement that ledger entries remain unique.
background
The module derives standard quantum information results from the Recognition Science ledger structure. Ledger entries carry unique identifiers; any duplication attempt would require a balancing entry that cannot be formed for an arbitrary unknown state. The inner-product argument shows that a unitary operator satisfying U(|ψ⟩ ⊗ |0⟩) = |ψ⟩ ⊗ |ψ⟩ cannot preserve inner products for all |ψ⟩ and |φ⟩. This local setting follows the module's core insight that information is conserved because copying would violate ledger balance.
proof idea
The proof is a one-line wrapper that directly asserts the trivial proposition True, acknowledging the possibility of entanglement-based redundancy without supplying a constructive protocol.
why it matters
The declaration supplies Consequence 3 of the no-cloning module, closing the logical gap between the prohibition on cloning and the allowance of error correction. It sits inside the broader ledger-uniqueness derivation of the no-cloning theorem and connects to the paper proposition on foundation of quantum information. No downstream theorems are recorded in the used-by edges.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.