Related papers: Extending Resource Monotones using Kan Extensions

Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalization of the theory of canonical extension to the setting of first order logic. We define a notion of…

Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols…

We define and study expansion problems on countable structures in the setting of descriptive combinatorics. We consider both expansions on countable Borel equivalence relations and on countable groups, in the Borel, measure and category…

This is a survey paper on the connection of enriched category theory over a quantale and tropical mathematics. Quantales or complete idempotent semirings, as well as matrices with coefficients in them, are fundamental objects in both…

This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the…

Quantum scrambling refers to the spread of local quantum information into the many degrees of freedom of a quantum system. In this work, we introduce a resource theory of scrambling which incorporates two mechanisms, "entanglement…

Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema…

How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act…

Categories can be identified -- up to isomorphism -- with polynomial comonads on Set. The left Kan extension of a functor along itself is always a comonad -- called the density comonad -- so it defines a category when its carrier is…

Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…

This paper develops a new framework, \emph{simultaneous saturation}, designed to quantify the size of sets whose elements are simultaneously large. The framework establishes a correspondence between the magnitude of such sets and a system…

Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in other areas of…

We introduce a calculus of extensional resource terms. These are resource terms \`a la Ehrhard-Regnier, but in infinitely eta-long form. The calculus still retains a finite syntax and dynamics: in particular, we prove strong confluence and…

The investigation and classification of non-unique factorization phenomena has attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P.A. Garc\'ia-S\'anchez, together with several co-authors, derived…

While there is general consensus on the definition of incompatible POVMs, moving up to the level of instruments one finds a much less clear situation, with mathematically different and logically independent definitions of incompatibility.…

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…

We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…

Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…

Using the functor of Baumslag rationalization of groups we construct a functor on the category of all (non necessarily simply connected) spaces that extends the classical rationalization of simply connected spaces. We study this functor and…

We define the concept of a monotonic theory and show how to build efficient SMT (SAT Modulo Theory) solvers, including effective theory propagation and clause learning, for such theories. We present examples showing that monotonic theories…