Related papers: Compactly accessible categories and quantum key di…
We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so…
The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general…
Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other…
Quantum key distribution is one of the most fundamental cryptographic protocols. Quantum walks are important primitives for computing. In this paper we take advantage of the properties of quantum walks to design new secure quantum key…
The theoretically proven security of quantum key distribution (QKD) could revolutionise how information exchange is protected in the future. Several field tests of QKD have proven it to be a reliable technology for cryptographic key…
Quantum Key Distribution (QKD) is an approach for establishing symmetrical binary keys between distant users in an information-theoretically secure way. In this paper we provide an overview of existing solutions that integrate QKD within…
We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…
The purpose of this paper is to consider some basic constructions in the category of compact quantum groups --for example de case of extensions, of Drinfeld twists, of matched pairs, of extensions, of linked pairs and of cocycle Singer…
We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in…
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…
Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we…
Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the…
We extend the notion of a factorization system in a category to the realm of $\infty$-categories. To this end, we provide a description of the category of $\infty$-categories with factorization systems as the category of presheaves of…
The dimension reduction method enables security proofs of quantum key distribution (QKD) protocols that are originally formulated in infinite dimensions via reduction to a tractable finite-dimensional optimization. The reduction of…
Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
Quantum communication over long distances is integral to information security and has been demonstrated in free space and fibre with two-dimensional polarisation states of light. Although increased bit rates can be achieved using…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
Practical implementations of Quantum Key Distribution (QKD) extending beyond urban areas commonly use satellite links. However, the transmission of quantum states through the Earth's atmosphere is highly susceptible to noise, restricting…