Related papers: Connectivity for quantum graphs
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
We present a strong connection between quantum information and quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show…
The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum…
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…
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
We propose a decision procedure for analysing security of quantum cryptographic protocols, combining a classical algebraic rewrite system for knowledge with an operational semantics for quantum distributed computing. As a test case, we use…
It is well--known that if one is given a principal $G$--bundle with a principal connection, then for every unitary finite--dimensional linear representation of $G$ one can induce a linear connection and a Hermitian structure on the…
Can complex classical systems be designed to exhibit superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to one map between the product basis of quantum states comprising an arbitrary number…
Society relies and depends increasingly on information exchange and communication. In the quantum world, security and privacy is a built-in feature for information processing. The essential ingredient for exploiting these quantum advantages…
The graph state formalism offers strong connections between quantum information processing and graph theory. Exploring these connections, first we show that any graph is a pivot-minor of a planar graph, and even a pivot minor of a…
In this work we show that given a connectivity graph $G$ of a $[[n,k,d]]$ quantum code, there exists $\{K_i\}_i, K_i \subset G$, such that $\sum_i |K_i|\in \Omega(k), \ |K_i| \in \Omega(d)$, and the $K_i$'s are $\tilde{\Omega}(…
Large-scale quantum networks with thousands of nodes require scalable network protocols and physical hardware to realize. In this work, we introduce packet switching as a new paradigm for quantum data transmission in both future and…
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.
Designing an operational architecture for the Quantum Internet is challenging in light of both fundamental limits imposed by physics laws and technological constraints. Here, we propose a method to abstract away most of the quantum-specific…
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
Quantum network is fragile to disturbances when qubits are transmitted through quantum channel. Reliability is an essential requirement for a quantum network and even the future quantum internet. A metric is needed to describe the…
The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during the last period, when a number of direct quantum coding theorems was discovered. To considerable extent…
We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…