How to make unforgeable money in generalised probabilistic 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.

arXiv comment27 pages, many diagrams. Comments welcome

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• Semi-Device Independent Quantum Money
• Universal structure of objective states in all fundamental causal theories
• On the impossibility of coin-flipping in generalized probabilistic theories via discretizations of semi-infinite programs
• Correlations constrained by composite measurements
• How dynamics constrains probabilities in general probabilistic theories
• Compositional resource theories of coherence
• Generalized dynamical theories in phase space and the hydrogen atom
• A no-go theorem for theories that decohere to quantum mechanics
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• Complete extension: the non-signaling analog of quantum purification
• Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions