Related papers: Bases in diagrammatic quantum protocols
In a recent article, the coordinate ring of the nodal cubic was given the structure of a quantum homogeneous space. Here the corresponding coalgebra Galois extension is expressed in terms of quantum groups at roots of unity, and is shown to…
We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riemannian manifold' based on quantum group principal bundles, a…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is…
We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…
Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these…
We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document…
In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We present a new template for building oblivious transfer from quantum information that we call the "fixed basis" framework. Our framework departs from prior work (eg., Crepeau and Kilian, FOCS '88) by fixing the correct choice of…
We give an algebraic presentation of directed acyclic graph structure, introducing a symmetric monoidal equational theory whose free PROP we characterise as that of finite abstract dags with input/output interfaces. Our development provides…
Traced monoidal categories are used to model processes that can feed their outputs back to their own inputs, abstracting iteration. The category of finite dimensional Hilbert spaces with the direct sum tensor is not traced. But…
We present a protocol for transferring arbitrary continuous-variable quantum states into a few discrete-variable qubits and back. The protocol is deterministic and utilizes only two-mode Rabi-type interactions which are readily available in…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Directed acyclic graphs (DAGs) are frequently used in epidemiology as a method to encode causal inference assumptions. We propose the DAGWOOD framework to bring many of those encoded assumptions to the forefront. DAGWOOD combines a root DAG…
We present a mathematical framework that unifies the quantum causal history formalism from theoretical high energy physics and the directed graph operator framework from the theory of operator algebras. The approach involves completely…
We define a diagrammatic monoidal category, together with a full and essentially surjective monoidal functor from this category to the category of modules over the exceptional Lie algebra of type $F_4$. In this way, we obtain a set of…
As the field of quantum physics evolves, researchers naturally form subgroups focusing on specialized problems. While this encourages in-depth exploration, it can limit the exchange of ideas across structurally similar problems in different…
Conventional wisdom suggests that realistic quantum repeaters will require quasi-deterministic sources of entangled photon pairs. In contrast, we here study a quantum repeater architecture that uses simple parametric down-conversion…
In this article, we discuss the optimality of basis transformations as a security measure for quantum key distribution protocols based on entanglement swapping. To estimate the security, we focus on the information an adversary obtains on…