quantum_cryptography_possible
plain-language theorem explainer
Quantum cryptography becomes possible once no-cloning is established, because any attempt to intercept and copy an unknown quantum key must disturb the ledger balance and become detectable. Workers in quantum information theory would cite the result as the direct bridge from Recognition Science ledger uniqueness to quantum key distribution. The proof is a one-line term-mode trivial assertion that records the consequence without further calculation.
Claim. No-cloning implies that eavesdropping on an unknown quantum state is detectable, thereby enabling quantum key distribution.
background
The module derives the quantum no-cloning theorem from ledger uniqueness: each ledger entry carries a unique identifier, copying requires a balancing entry, and arbitrary duplication is forbidden because the total information is conserved. The local setting is given by the module doc-comment: 'Derive the quantum no-cloning theorem from Recognition Science's ledger structure' with the explicit statement that 'no-cloning emerges from ledger uniqueness.' Upstream results supply the supporting primitives (collision-free empirical programs, primitive distinctions, edge lengths from psi, mechanism design, and mock theta structures) but are not invoked inside the trivial proof.
proof idea
The declaration is a term-mode proof consisting of the single identifier trivial. It functions as a one-line wrapper that records the logical consequence of the no-cloning result already established in the same module.
why it matters
The theorem supplies Consequence 1 of the module ('Quantum cryptography is possible. If you could clone, you could intercept and copy quantum keys') and therefore sits inside the information-theoretic branch of the Recognition framework. It connects the ledger-uniqueness argument directly to the practical claim that quantum key distribution is feasible. No downstream uses are recorded, leaving the result as a terminal remark rather than an active lemma.
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