Related papers: Quantale-Enriched Multicategories Via Actions
An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.
We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum…
Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of…
The linear quantile-quantile relationship provides an easy-to-implement yet effective tool for transformation to and testing for normality. Its good performance is verified in this report.
We consider two-stage hybrid protocols that combine quantum resource and classical resource to generate classical correlations shared by two separated players. Our motivation is twofold. First, in the near future the scale of quantum…
Standard formulations of quantum theory are based on complex numbers: Quantum states can be in superpositions, with weights given by complex probability amplitudes. Motivated by quantum theory promising a range of practical advantages over…
Phenomena induced by the existence of entanglement, such as nonlocal correlations, exhibit characteristic properties of quantum mechanics distinguishing from classical theories. When entanglement is accompanied by classical communication,…
We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an S-indexed monoidal category V. This includes classical enriched categories, indexed and fibered…
We consider monoids equipped with a compatible quantale valued relation, to which we call quantale enriched monoids, and study semidirect products of such structures. It is well-known that semidirect products of monoids are closely related…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
We determine the capacity of compound classical-quantum channels. As a consequence we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical…
For a small involutive quantaloid $\mathcal{Q}$, it is shown that the category of separated complete $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-functors is strictly monadic over the category of symmetric…
We prove, in a multipartite setting, that it's always feasible to exactly transform a genuinely $m$-partite entangled state with sufficient many copies to any other $m$-partite state via local quantum operation and classical communication.…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
We formulate an elementary condition on an involutive quantaloid Q under which there is a distributive law from the Cauchy completion monad over the symmetrisation comonad on the category of Q-enriched categories. For such quantaloids,…
Coherent information quantifies the achievable rate of the reliable quantum information transmission through a communication channel. Use of the correlated quantum states instead of the factorized ones may result in an increase in the…
We give a sufficient condition for quantising integrable systems.
Let $\mathfrak{C}$ be a multifusion 2-category. We show that every finite semisimple $\mathfrak{C}$-module 2-category is canonically enriched over $\mathfrak{C}$. Using this enrichment, we prove that every finite semisimple…
We introduce various measures of forward classical communication for bipartite quantum channels. Since a point-to-point channel is a special case of a bipartite channel, the measures reduce to measures of classical communication for…
When classical information is sent through a quantum channel of nonorthogonal states, there is a possibility that transmittable classical information exceeds a channel capacity in a single use of the initial channel by extending it into…