approximate_cloning_bound
plain-language theorem explainer
The declaration sets the highest fidelity for approximate 1-to-2 qubit cloning at exactly 5/6 inside the Recognition Science ledger model. Quantum information researchers working from ledger uniqueness would cite this numerical bound when quantifying imperfect cloning limits. The proof is a one-line reflexivity on the definition of optimalCloningFidelity.
Claim. The optimal fidelity of any approximate cloning map that takes an unknown qubit state to two copies is exactly $5/6$.
background
Recognition Science derives the no-cloning theorem from ledger uniqueness: each entry carries a unique identifier, and duplication would require a balancing entry that cannot be formed without knowledge of the original state. The module INFO-006 states that information is conserved and that copying an arbitrary unknown state |ψ⟩ would violate inner-product preservation. Upstream, optimalCloningFidelity is introduced as the noncomputable real constant 5/6 that bounds imperfect cloning; related ledger quantities such as the active edge count A appear in the dependency list but are not invoked here.
proof idea
The proof is a one-line reflexivity that equates the theorem goal directly to the definition of optimalCloningFidelity.
why it matters
This supplies the concrete numerical value required by the INFO-006 derivation of no-cloning from ledger structure. It anchors the approximate-cloning statement that precedes the falsification criteria listed in the module. The bound supports later claims about quantum cryptography and measurement disturbance without adding new axioms.
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