Ratio Map, Operator Fixed Points, and Multi-Ratio Protocol Design in Dynamical-Decoupling Noise Spectroscopy

Key Points

• This work aims to derive and analyze the ratio map in the context of dynamical-decoupling noise spectroscopy.
• Developed combinatorial origins of the ratio map R(α).
• Analyzed Parseval weight structure and logistical representations.
• Designed a multi-ratio protocol framework based on operator mean representations.
• Introduced a novel ratio map that aids in noise spectroscopy analysis.
• Establishes connections between ratio maps and Fisher/fragility geometry.
• Provides a structured design for implementing multi-ratio protocols.