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Related papers: Quantale-Enriched Multicategories Via Actions

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In this communication we generalize some recent results of Rump to categories enriched in a commutative quantale V. Using these results, we show that every quantale-enriched multicategory admits an injective hull. Finally, we expose a…

Category Theory · Mathematics 2021-06-25 Eros Martinelli

Building on our previous work on enriched regular logic, we introduce an enriched version of positive logic and relate it to enriched cone-injectivity classes and enriched accessible categories. To do this, we need a factorization system on…

Category Theory · Mathematics 2025-09-25 Jiří Rosický , Giacomo Tendas

We calculate the entanglement-assisted classical capacity of symmetric and asymmetric Pauli channels where two consecutive uses of the channels are correlated. It is evident from our study that in the presence of memory, a higher amount of…

Quantum Physics · Physics 2009-11-13 Nigum Arshed , A. H. Toor

For a small quantaloid $\mathcal{Q}$, we introduce $\mathcal{M}$-(co)complete $\mathcal{Q}$-categories, i.e., (co)complete $\mathcal{Q}$-categories up to Morita equivalence, as Eilenberg--Moore algebras of the presheaf monad on the category…

Category Theory · Mathematics 2025-11-24 Xiaoye Tang

Quantum channels are known to provide qualitatively better information transfer capacities over their classical counterparts. Examples include quantum cryptography, quantum dense coding, and quantum teleportation. This is a short review on…

Quantum Physics · Physics 2015-03-19 Aditi Sen De , Ujjwal Sen

There are two ways to describe the interaction between classical and quantum information categorically: one based on completely positive maps between Frobenius algebras, the other using symmetric monoidal 2-categories. This paper makes a…

Quantum Physics · Physics 2014-12-31 Chris Heunen , Jamie Vicary , Linde Wester

We prove that a Quillen adjunction of model categories (of which we do not require functorial factorizations and of which we only require finite bicompleteness) induces a canonical adjunction of underlying quasicategories.

Category Theory · Mathematics 2015-01-14 Aaron Mazel-Gee

We investigate the quantum advantage that can arise in typical two-party communication scenarios, where the sender and the receiver are allowed to share prior correlations. Focusing on communication tasks constrained by the…

Quantum Physics · Physics 2026-03-20 Satyaki Manna , Ankush Pandit , Debashis Saha

Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with…

Category Theory · Mathematics 2017-05-25 Dirk Hofmann , Carla Reis

We investigate two senders and one receiver multiparty communication scenario. Following Phys.Rev.A83, 062112 and arXiv : 2506.07699, we study multiparty communication bounded by dimension and distinguishability. We provide an explicit…

Quantum Physics · Physics 2025-12-08 Ankush Pandit

We prove that there is an adjunction between what we call \'etale topological categories and restriction quantal frames that leads to an adjunction with a category of complete restriction monoids. This generalizes the adjunction between…

Category Theory · Mathematics 2023-03-10 Mark V. Lawson

The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…

Quantum Physics · Physics 2017-07-20 Katja Ried , Jean-Philippe W. MacLean , Robert W. Spekkens , Kevin J. Resch

For an arbitrary localic etale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of G-actions is…

Category Theory · Mathematics 2011-03-29 Pedro Resende

This is an elaboration about the "extra" advantage of the performance of quantized physical systems over classical ones; both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based upon…

Quantum Physics · Physics 2020-06-19 Karl Svozil

This was significantly extended from the previous article quant-ph/9705043,especially in an information theoretic aspect, by adding new results.

Quantum Physics · Physics 2009-10-31 Masahide Sasaki , Kentaro Kato , Masayuki Izutsu , Osamu Hirota

The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and…

Mathematical Physics · Physics 2013-05-29 A. S. Holevo , M. E. Shirokov

We introduce the notion of an enriched fibration, i.e. a fibration whose total category and base category are enriched in those of a monoidal fibration in an appropriate way. Furthermore, we provide a way to obtain such a structure,…

Category Theory · Mathematics 2018-07-09 Christina Vasilakopoulou

In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.

Algebraic Topology · Mathematics 2022-05-16 Lauren Bandklayder , Julia E. Bergner , Rhiannon Griffiths , Brenda Johnson , Rekha Santhanam

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…

Quantum Physics · Physics 2008-09-03 B. Georgeot , O. Giraud

Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Quantum Mechanics (QM) has already shown its effectiveness in many fields and…