Equal-Superposition Coherence Decay

Abstract

Strict phase damping drives equal-superposition coherence to zero.

Theorem 1.1 (Equal-superposition coherence tends to zero).

$$\underset{N\to \infty }{\lim }\mathrm{phaseDampingIterate}(c,N,\mathrm{equalSuperpositionDensity}{)}_{01}=0$$

Proof. Machine-checked in Lean as D5/S3/Quantum/Decoherence/CoherenceDecay.equal_superposition_coherence_tendsto_zero (✓ std3). ∎

Citation. Wojciech H. Zurek (2003). Decoherence, einselection, and the quantum origins of the classical. DOI: 10.1103/RevModPhys.75.715.

Commentary.

For a real phase-damping retention coefficient c in [0,1), the exact finite-step certificate identifies the equal-superposition off-diagonal entry with (1/2)c^N. Pinned Mathlib’s geometric-power limit then sends that entry to zero. This closes only the source atom’s exact coherence-decay clause; it does not derive the channel from a Hamiltonian or formalize the atom’s center, pointer-basis, or redundancy claims.

References

• Truth anchor: D5/S3/Quantum/Decoherence/CoherenceDecay.equal_superposition_coherence_tendsto_zero
• Dependency: D5/S3/Quantum/QubitWitnesses