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Unique Information and Secret Key Agreement.

Ryan G James1, Jeffrey Emenheiser1, James P Crutchfield1

  • 1Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.

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Partial Information Decomposition (PID) quantifies source variable influence on a target. Using secret key agreement rates from cryptography, this study finds inconsistencies with PID, suggesting a directional interpretation and revealing new connections.

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cryptographyinformation theorypartial information decompositionsecret key agreement

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Area of Science:

  • Information Theory
  • Cryptography
  • Machine Learning

Background:

  • Partial Information Decomposition (PID) aims to quantify information flow from multiple sources to a target.
  • Existing PID frameworks face challenges in consistently quantifying unique and synergistic information components.

Purpose of the Study:

  • To investigate the operationalization of PID components using secret key agreement rates from cryptography.
  • To address inconsistencies in PID quantification and propose a more robust framework.

Main Methods:

  • Applied secret key agreement rates, a cryptographic concept, to quantify unique information in PID.
  • Analyzed the consistency of different secret key agreement rate forms with PID principles.
  • Investigated connections between third-order connected information, two-way secret key agreement rate, and synergy.

Main Results:

  • Demonstrated that three of four secret key agreement rate forms are inconsistent with PID.
  • Identified a consistent form that implies a directional interpretation of PID.
  • Revealed a novel link between third-order connected information, two-way secret key agreement rate, and synergy.

Conclusions:

  • Secret key agreement rates offer a promising, albeit complex, approach to quantifying PID.
  • A consistent PID framework necessitates explicit directional interpretations.
  • Further research is needed to resolve challenges in PID quantification and its applications.