How to make unforgeable money in generalised probabilistic theories

John H. Selby and Jamie Sikora

Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, N2L 2Y5

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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.

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Cited by

[1] Jamie Sikora and John H. Selby, "Impossibility of coin flipping in generalized probabilistic theories via discretizations of semi-infinite programs", Physical Review Research 2 4, 043128 (2020).

[2] Thomas D. Galley and Lluis Masanes, "How dynamics constrains probabilities in general probabilistic theories", Quantum 5, 457 (2021).

[3] Damián Pitalúa-García, "Spacetime symmetries and the qubit Bloch ball: A physical derivation of finite-dimensional quantum theory and the number of spatial dimensions", Physical Review A 104 3, 032220 (2021).

[4] Ciarán M. Lee and John H. Selby, "A no-go theorem for theories that decohere to quantum mechanics", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474 2214, 20170732 (2018).

[5] Marius Krumm, "What can we learn from trivial measurements?", Quantum Views 3, 17 (2019).

[6] John H. Selby and Ciarán M. Lee, "Compositional resource theories of coherence", arXiv:1911.04513, Quantum 4, 319 (2020).

[7] Karol Horodecki and Maciej Stankiewicz, "Semi-device-independent quantum money", New Journal of Physics 22 2, 023007 (2020).

[8] Carlo Maria Scandolo, Roberto Salazar, Jarosław K. Korbicz, and Paweł Horodecki, "Universal structure of objective states in all fundamental causal theories", Physical Review Research 3 3, 033148 (2021).

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The above citations are from Crossref's cited-by service (last updated successfully 2021-10-20 07:17:52) and SAO/NASA ADS (last updated successfully 2021-10-20 07:17:53). The list may be incomplete as not all publishers provide suitable and complete citation data.