17 citations · 98 across the 21 of their papers we have counts for
21 papers
UC, Categorically: Rigorous Diagrammatic Proofs
Pooya Farshim, Martti Karvonen, Andre Knispel +2
Category theory is a mathematical theory of composition, widely used in logic, computing, and physics. Here we apply it to give a theory of secure composition. In particular, we pr…
Algebraic paradoxes in adaptive quantum computation
Samson Abramsky, Rui Soares Barbosa, Carmen Constantin +1
Measurement-based quantum computation (MBQC) is a universal model of quantum computation whose full power requires adaptivity. Contextuality is known to power quantum advantage in…
Comment on 'The axiom of choice and the no-signalling principle'
Martti Karvonen
The main claim of Baumeler et al. (Proc. R. Soc. A 481, 20240601; arXiv:2206.08467) is that "functional (deterministic) no-signalling resources can be stronger than probabilistic o…
Why cut-and-choose quantum state verification cannot be both efficient and secure
Fabian Wiesner, Ziad Chaoui, Diana Kessler +2
Quantum state verification plays a vital role in many quantum cryptographic protocols, as it allows the use of quantum states from untrusted sources. While some progress has been m…
Why quantum state verification cannot be both efficient and secure: a categorical approach
Fabian Wiesner, Ziad Chaoui, Diana Kessler +2
The advantage of quantum protocols lies in the inherent properties of the shared quantum states. These states are sometimes provided by sources that are not trusted, and therefore…
Inner automorphisms as 2-cells
Pieter Hofstra, Martti Karvonen
Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connect…
Towards a Unified Theory of Time-Varying Data
Benjamin Merlin Bumpus, James Fairbanks, Martti Karvonen +2
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a gene…
Uncloneable Quantum Advice
Anne Broadbent, Martti Karvonen, Sébastien Lord
The famous no-cloning principle has been shown recently to enable a number of uncloneable functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the…
Categorical composable cryptography: extended version
Anne Broadbent, Martti Karvonen
We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus gi…
Inner autoequivalences in general and those of monoidal categories in particular
Pieter Hofstra, Martti Karvonen
We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how…
Categorical composable cryptography
Anne Broadbent, Martti Karvonen
We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus gi…
Closing Bell: Boxing black box simulations in the resource theory of contextuality
Rui Soares Barbosa, Martti Karvonen, Shane Mansfield
This chapter contains an exposition of the sheaf-theoretic framework for contextuality emphasising resource-theoretic aspects, as well as some original results on this topic. In pa…
Neither Contextuality nor Nonlocality Admits Catalysts
Martti Karvonen
We show that the resource theory of contextuality does not admit catalysts, i.e., there are no correlations that can enable an otherwise impossible resource conversion and still be…
The Way of the Dagger
Martti Karvonen
A dagger category is a category equipped with a functorial way of reversing morphisms, i.e. a contravariant involutive identity-on-objects endofunctor. Dagger categories with addit…
A comonadic view of simulation and quantum resources
Samson Abramsky, Rui Soares Barbosa, Martti Karvonen +1
We study simulation and quantum resources in the setting of the sheaf-theoretic approach to contextuality and non-locality. Resources are viewed behaviourally, as empirical models.…
Reversible effects as inverse arrows
Chris Heunen, Robin Kaarsgaard, Martti Karvonen
Reversible computing models settings in which all processes can be reversed. Applications include low-power computing, quantum computing, and robotics. It is unclear how to represe…
Categories of Empirical Models
Martti Karvonen
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve usi…
Limits in dagger categories
Chris Heunen, Martti Karvonen
We develop a notion of limit for dagger categories, that we show is suitable in the following ways: it subsumes special cases known from the literature; dagger limits are unique up…
Biproducts without pointedness
Martti Karvonen
We show how to define biproducts up to isomorphism in an arbitrary category without assuming any enrichment. The resulting notion coincides with the usual definitions whenever all…
Monads on dagger categories
Chris Heunen, Martti Karvonen
The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when everything respects the dagger: the monad and…
Reversible monadic computing
Chris Heunen, Martti Karvonen
We extend categorical semantics of monadic programming to reversible computing, by considering monoidal closed dagger categories: the dagger gives reversibility, whereas closure gi…