Related papers: Quantale-Enriched Multicategories Via Actions
For quantum states of two subsystems, entanglement measures are related to capacities of communication tasks -- highly entangled states give higher capacity of transmitting classical as well as quantum information. However, we show that…
In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
Classical communication through quantum channels may be enhanced by sharing entanglement. Superdense coding allows the encoding, and transmission, of up to two classical bits of information in a single qubit. In this paper, the maximum…
We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…
We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their…
We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between…
We compare two possible ways of defining a category of 1-combs, the first intensionally as coend optics and the second extensionally as a quotient by the operational behaviour of 1-combs on lower-order maps. We show that there is a full and…
Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the…
We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. The aim of the paper is to justify and contextualize the new notion by…
We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a…
We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…
In order to reason about effects, we can define quantitative formulas to describe behavioural aspects of effectful programs. These formulas can for example express probabilities that (or sets of correct starting states for which) a program…
Originally enriched categories were defined over a monoidal category, but it was gradually realized that important examples can only be included when one enriches over more general structures such as bicategories and virtual double…
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with…
We consider the problem of trying to send a single classical bit through a noisy quantum channel when two transmissions through the channel are available as a resource. Classically, two transmissions add nothing to the receiver's capability…
In this work we successfully present a quantum version of the multiplayer Colonel Blotto game. We find that players with access to the quantum strategies has a advantage over the classical ones. The payoff is invariant under the order of…
We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in…
We establish the feasibility of investigating the theory of $R\text{-}\mathrm{Mod}$-enriched categories, for any commutative and unitary ring $R$, through the framework of $\mathbb{A}\mathrm{b}$-enriched category theory. In particular, we…
We show that for two initially excited qubits, interacting via dipole forces and with a common reservoir, entanglement is preceded by the emergence of quantum and classical correlations. After a time lag, entanglement finally starts…