# Taking a Lesson from Quantum Particles for Statistical Data Privacy

## TL;DR

This paper introduces a novel information-theoretic privacy framework leveraging Fisher information, linking privacy-utility trade-offs to quantum mechanics principles, and proposing a systematic method for privacy parameter setting.

## Contribution

It extends information-theoretic privacy using Fisher information to avoid prior data assumptions and connects privacy optimization to solving Schrödinger's equation.

## Key findings

- Optimal privacy noise follows Schrödinger's equation
- Established a privacy-utility trade-off akin to Heisenberg's uncertainty
- Proposed a systematic approach for privacy parameter setting

## Abstract

Privacy is under threat from artificial intelligence revolution fueled by unprecedented abundance of data. Differential privacy, an established candidate for privacy protection, is susceptible to adversarial attacks, acts conservatively, and leads to miss-implementations because of lacking systematic methods for setting its parameters (known as the privacy budget). An alternative is information-theoretic privacy using entropy with the drawback of requiring prior distribution of the private data. Here, by using the Fisher information, information-theoretic privacy framework is extended to avoid unnecessary assumptions on the private data. The optimal privacy-preserving additive noise, extracted by minimizing the Fisher information, must follow the time-independent Schrodinger's equation. A fundamental trade-off between privacy and utility is also proved, reminiscent of the Heisenberg uncertainty principle.