How to make unforgeable money in generalised probabilistic theories

TL;DR

This paper explores the theoretical possibility of creating unforgeable money within generalised probabilistic theories, extending quantum security concepts to broader physical frameworks using cone programming.

Contribution

It demonstrates that under certain conditions, unforgeable money can be constructed in generalised theories, generalizing quantum money security proofs with cone programming techniques.

Findings

Unforgeability can be achieved with exponentially small counterfeiting probability.

The framework applies to a wide range of physical theories beyond quantum mechanics.

Cone programming is effective in analyzing security within these theories.

Abstract

We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for quantum money which have their security based on the validity of quantum mechanics. In this work, we examine Wiesner's money scheme in the framework of generalised probabilistic theories. This framework is broad enough to allow for essentially any potential theory of nature, provided that it admits an operational description. We prove that under a quantifiable version of the no-cloning theorem, one can create physical money which has an exponentially small chance of being counterfeited. Our proof relies on cone programming, a natural generalisation of semidefinite programming. Moreover, we discuss some of the difficulties that arise when considering non-quantum theories.