The Coherence-Time Density Operator: A Spacetime Threshold Observable for Gate Stability in the Δ-Gate Formalism (Paper VI/VII)

Key Points

• This research aims to define a coherence-time density operator as a tool for assessing quantum gate stability.
• Introduced a coherence-time density operator ρ_K(t) as a threshold observable for gate stability.
• Proved Lindblad dephasing recovery in a spatially uniform limit.
• Derived thresholds for distance-d repetition codes.
• Embedded findings from five companion papers into the main analysis.
• Investigated the effects of Lorentz boosts on gate lifetimes and established a frame-invariant threshold.
• A Δ-Gate maintains activity when ρ_K(t) is greater than or equal to a defined minimum value ρ_K,min.
• Explicit thresholds for distance-d repetition codes were derived for gate stability.
• The framework provides seven falsifiable predictions regarding quantum gate behavior under various conditions.