quantumErrorCorrection
Quantum error correction receives a concise label here as protection of states via redundancy and syndromes, realized through 8-tick phase correlations in Recognition Science. Information theorists deriving bounds from the eight-tick octave would cite this when extending Shannon capacity to quantum regimes. The implementation is a direct string assignment accompanied by a note on entanglement and syndrome measurement.
claimQuantum error correction is the mechanism that safeguards quantum states through redundancy and syndrome extraction, where the eight-tick phase structure supplies natural correlations that tolerate continuous errors without cloning or disturbance-free measurement.
background
The module INFO-005 derives error-correction bounds from the eight-tick structure. Classical transmission faces noise that corrupts data; redundancy permits recovery, and Shannon capacity gives the maximum reliable rate. In Recognition Science the eight-tick phases (T7) encode each bit across correlated phases, turning phase correlations into built-in redundancy.
proof idea
One-line definition that directly assigns the descriptive string literal for quantum error correction in the 8-tick setting.
why it matters in Recognition Science
The definition supplies the quantum counterpart to the module's classical bounds (hamming_bound_8tick, singleton_bound_8tick). It fills the T7 eight-tick octave step by noting how phase correlations enable QEC despite no-cloning and continuous errors, anchoring the transition from classical to quantum information within the Recognition framework.
scope and limits
- Does not derive quantitative error thresholds or capacities.
- Does not formalize entanglement or syndrome operators.
- Does not connect to phi-ladder mass formulas or alpha-band constants.
- Does not prove existence or optimality of any code.
formal statement (Lean)
138def quantumErrorCorrection : String :=
proof body
Definition body.
139 "Protect quantum states using redundancy and syndromes"
140
141/-- For majority voting on 8 phases, the threshold is p < 3/8.
142 Below this error rate, the majority is always correct. -/