How to make unforgeable money in generalised probabilistic theories

Selby, John H.; Sikora, Jamie

doi:10.22331/q-2018-11-02-103

Cited by 21 publications

(18 citation statements)

References 32 publications

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“…Furthermore, Selby and Sikora [30] analyzed unforgeable money in the Generalized Probabilistic Theories. We should also point out experimental results in the quantum money field were presented by three groups of Bartkiewicz et al [31], Bozzio et al [32], and Guan et al [33] respectively.…”

Section: Private-key Quantum Moneymentioning

confidence: 99%

“…It is however plausible that if the quantum version of the OCG law turns out to be accurate, the individuals will tend to keep the most secure, cheapest to produce and to store money of the highest commodity value (in the sense of its use for quantum information processing), and will spend the other currencies more often. Going a bit further, one can consider monies in a theory T (for such a general approach see [30]), and have a 'T Oresme-Copernicus-Gresham's law', a theory-dependent version describing the flow of currencies valid in theory T. An interesting particular case would be the 'multi-theory OCG law' that could govern the flow of currencies between different sub-theories. A natural example of the latter would be Classical-Quantum Oresme-Copernicus-Gresham's law, expressing the behavior of classical currencies and the quantum ones on the same footing.…”

Section: Quantum Oresme-copernicus-gresham's Lawmentioning

confidence: 99%

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Semi-device-independent quantum money

Horodecki

Stankiewicz

2020

New J. Phys.

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The seminal idea of quantum money, not forgeable due to laws of Quantum Mechanics, proposed by Stephen Wiesner, has laid the foundations for the Quantum Information Theory in the early '70s.Recently, several other schemes for quantum currencies have been proposed, all, however, relying on the assumption that the quantum source device, acts according to its specification. This makes several known quantum money protocols vulnerable to the so-called hardware Trojan horse attacks. We, therefore, study the following problem: to what extent quantum money schemes can be made independent from the inner working of source and verification-devices used by the honest parties (bank and mint) in creating and processing the quantum money? Drawing inspirations from the semi-device-independent quantum key distribution protocol, we introduce the first scheme of quantum money with this assumption partially relaxed, along with the proof of its unforgeability. Finally, we formulate and discuss a quantum analog of the Oresme-Copernicus-Gresham's law of economy, that may hold in the future.

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Section: Private-key Quantum Moneymentioning

confidence: 99%

Section: Quantum Oresme-copernicus-gresham's Lawmentioning

confidence: 99%

Semi-device-independent quantum money

Horodecki

Stankiewicz

2020

New J. Phys.

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“…A, A A (73) where A is a system in P and is an idempotent on A. We introduce the shorthand notation for systems: (74) and, noting that there can be multiple different idempotents per system we will distinguish them by their colour, hence we can have systems such as A and A which differ only by their associated idempotent.…”

Section: Definition 5 (Karoubi Envelope K) Systems Labeled In K[p] mentioning

confidence: 99%

“…This last point is useful as it provides the ability to characterise coherence in operational and physical terms, rather than via specific features of the mathematical formalism of quantum theory-such as Hilbert spaces and complex numbers. There is some existing work on studying resource theories in generalised theories such as [46,14,15,86,4] and this general approach has also been of use to deepen our understanding of computation [52,47,9,31,6,54,55,50,51], cryptography [77,74,48,78,7,5,53,49] and much more.…”

Section: Introductionmentioning

confidence: 99%

Compositional resource theories of coherence

Selby

Lee

2020

Quantum

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Quantum coherence is one of the most important resources in quantum information theory. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers. Recently, there has been substantial progress in developing mathematical resource theories of coherence, paving the way towards its quantification and control. To date however, these resource theories have only been mathematically formalised within the realms of convex-geometry, information theory, and linear algebra. This approach is limited in scope, and makes it difficult to generalise beyond resource theories of coherence for single system quantum states. In this paper we take a complementary perspective, showing that resource theories of coherence can instead be defined purely compositionally, that is, working with the mathematics of process theories, string diagrams and category theory. This new perspective offers several advantages: i) it unifies various existing approaches to the study of coherence, for example, subsuming both speakable and unspeakable coherence; ii) it provides a general treatment of the compositional multi-system setting; iii) it generalises immediately to the case of quantum channels, measurements, instruments, and beyond rather than just states; iv) it can easily be generalised to the setting where there are multiple distinct sources of decoherence; and, iv) it directly extends to arbitrary process theories, for example, generalised probabilistic theories and Spekkens toy model---providing the ability to operationally characterise coherence rather than relying on specific mathematical features of quantum theory for its description. More importantly, by providing a new, complementary, perspective on the resource of coherence, this work opens the door to the development of novel tools which would not be accessible from the linear algebraic mind set.

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“…Current treatments have tended to emphasise finite dimensional systems and system composition. Using this framework (or related frameworks such as convex operational theories [19,20] and operational probabilistic theories [21]) many physical and informational features of general probabilistic theories have been studied, such as interference phenomena [22][23][24][25], computation [26,27], thermodynamics [28][29][30] and others [31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

How dynamics constrains probabilities in general probabilistic theories

Galley

Masanes

2021

Quantum

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We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with the action of the reversible dynamics, whilst the probabilistic structure determines the measurements and the outcome probabilities. For transitive dynamical structures whose dynamical group and stabiliser subgroup form a Gelfand pair we show that all probabilistic structures are rigid (cannot be infinitesimally deformed) and are in one-to-one correspondence with the spherical representations of the dynamical group. We apply our methods to classify all probabilistic structures when the dynamical structure is that of complex Grassmann manifolds acted on by the unitary group. This is a generalisation of quantum theory where the pure states, instead of being represented by one-dimensional subspaces of a complex vector space, are represented by subspaces of a fixed dimension larger than one. We also show that systems with compact two-point homogeneous dynamical structures (i.e. every pair of pure states with a given distance can be reversibly transformed to any other pair of pure states with the same distance), which include systems corresponding to Euclidean Jordan Algebras, all have rigid probabilistic structures.

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How to make unforgeable money in generalised probabilistic theories

Cited by 21 publications

References 32 publications

Semi-device-independent quantum money

Semi-device-independent quantum money

Compositional resource theories of coherence

How dynamics constrains probabilities in general probabilistic theories

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