Related papers: Compactly accessible categories and quantum key di…
Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction…
Quantum Key Distribution (QKD) is a technology that ensures secure communication by leveraging the principles of quantum mechanics, such as the no-cloning theorem and quantum uncertainty. This chapter provides an overview of this quantum…
In this paper we redevelop the foundations of the category theory of quasi-categories (also called infinity-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi-categories admits certain weak 2-limits, among…
Modern communication strives towards provably secure systems which can be widely deployed. Quantum key distribution provides a methodology to verify the integrity and security of a key exchange based on physical laws. However, physical…
As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is…
Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device and channel noises has been missing.…
Quantum Key Distribution (QKD) supports the negotiation and sharing of private keys with unconditional security between authorized parties. Over the years, theoretical advances and experimental demonstrations have successfully transitioned…
Quantum key distribution (QKD) systems require optimal performance of both quantum and classical channels - utilizing as few as possible qubits and bits for establishing as many as possible key bits. Here we report a way to determine if a…
Quantum key distribution (QKD) together with one time pad encoding can provide information-theoretical security for communication. Currently, though QKD has been widely deployed in many metropolitan fiber networks, its implementation in a…
Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.
It is shown that, for a small quantaloid Q, the category of small Q-categories and Q-functors is total and cototal, and so is the category of Q-distributors and Q-Chu transforms.
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
It is known that monoidal categories have a finite definition, whereas multicategories have an infinite (albeit finitary) definition. Since monoidal categories correspond to representable multicategories, it goes without saying that…
In this article, we review several aspects of composability in the context of quantum cryptography. The first part is devoted to key distribution. We discuss the security criteria that a quantum key distribution protocol must fulfill to…
Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from…
De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and…
We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel…