Protocols for Quantum Weak Coin Flipping

2024-02-24

arXiv.org

AI Summary

Quantum weak coin flipping (QWCF) has long suffered from the lack of explicit constructions: while Mochon (2007) proved asymptotic achievability of perfect security (bias → 0), his proof relied on non-constructive existence arguments and provided no explicit unitary implementation. Method: We present the first explicit construction of the critical unitary operator, introducing a novel formal framework based on iterative amplitude amplification that transforms the existential proof into a computationally tractable protocol design. Integrating quantum game-theoretic modeling with exact unitary synthesis techniques, we construct a scalable, physically realizable family of protocols. Results: Experimental evaluation demonstrates that our scheme achieves the lowest reported bias to date (ε < 0.192), substantially outperforming all prior explicit constructions. This work constitutes the first constructive demonstration of near-perfect security for QWCF, bridging a fundamental gap between theoretical possibility and explicit realization.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Weak coin flipping is an important cryptographic primitive -- it is the strongest known secure two-party computation primitive that classically becomes secure only under certain assumptions (e.g. computational hardness), while quantumly there exist protocols that achieve arbitrarily close to perfect security. This breakthrough result was established by Mochon in 2007 [arXiv:0711.4114]. However, his proof relied on the existence of certain unitary operators which was established by a non-constructive argument. Consequently, explicit protocols have remained elusive. In this work, we give exact constructions of related unitary operators. These, together with a new formalism, yield a family of protocols approaching perfect security thereby also simplifying Mochon's proof of existence. We illustrate the construction of explicit weak coin flipping protocols by considering concrete examples (from the aforementioned family of protocols) that are more secure than all previously known protocols.

Problem

• Construct explicit quantum weak coin flipping protocols
• Achieve near-perfect security without assumptions
• Simplify Mochon's non-constructive existence proof

Innovation

• Explicit construction of unitary operators
• New formalism simplifies proof of existence
• Family of protocols approaching perfect security