Related papers: Resource convertibility and ordered commutative mo…

We aim to counter the tendency for specialization in science by advancing a language that can facilitate the translation of ideas and methods between disparate contexts. The focus is on questions of "resource-theoretic nature". In a…

In many different fields of science, it is useful to characterize physical states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent…

There are countless sources of data available to governments, companies, and citizens, which can be combined for good or evil. We analyse the concepts of combining data from common sources and linking data from different sources. We model…

Quantum resource theory is a cutting-edge tool used to study practical implementations of quantum mechanical principles under realistic operational constraints. It does this by modelling quantum systems as restricted classes of possible or…

A series of recent works has shown that placing communication channels in a coherent superposition of alternative configurations can boost their ability to transmit information. Instances of this phenomenon are the advantages arising from…

Commutative totally ordered monoids abound, number systems for example. When the monoid is not assumed commutative, one may be hard pressed to find an example. One suggested by Professor Orr Shalit are the countable ordinals with addition.…

Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paper we devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information.…

Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms.…

In this paper, we study the machine learning elements which we are interested in together as a machine learning system, consisting of a collection of machine learning elements and a collection of relations between the elements. The…

A central problem in the study of resource theories is to find functions that are nonincreasing under resource conversions - termed monotones - in order to quantify resourcefulness. Various constructions of monotones appear in many…

Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting --…

The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this…

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 difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking. We develop a general approach to this…

A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint,…

Quantum coherence is one of the most important resources in quantum information. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers.…

Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders. These may be the key resource for experimental violations of causal inequalities and have been recently identified as…

Quantum information processing relies on a variety of resources, including entanglement, coherence, non-Gaussianity, and magic. In realistic settings, protocols run on networks of parties with heterogeneous local resource constraints, so…

We identify the algebraic structure of the material histories generated by concurrent processes. Specifically, we extend existing categorical theories of resource convertibility to capture concurrent interaction. Our formalism admits an…

Quantum coherence and other non-classical features are widely discussed in chemical dynamics, yet it remains difficult to quantify when such resources are operationally relevant for a given process and observable. While quantum resource…