Related papers: Construction and Rigorous Analysis of Quantum-Like…
This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states,…
The generation of a large amount of entanglement is a necessary condition for a quantum computer to achieve quantum advantage. In this paper, we propose a method to efficiently generate pseudo-random quantum states, for which the degree of…
We proposed two classes of multiparticle entangled states, the multigraph states and multihypergraph states, defined by unique operations on the edges and hyperedges. A key discovery is the one-to-one correspondence between the proposed…
Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite…
Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement…
Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve…
We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory. In these setups, the paths of photons are identified such that the photon-source information is never created.…
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…
Indistinguishability of identical particles is a resource for quantum information processing and has been utilized to generate entanglement from independent particles that spatially overlap only at the detection stage. Here we provide a…
Recent advances have led towards first prototypes of quantum networks in which entanglement is distributed by sources producing bipartite entangled states. This raises the question of which states can be generated in quantum networks based…
We build a machine learning model to detect correlations in a three-qubit system using a neural network trained in an unsupervised manner on randomly generated states. The network is forced to recognize separable states, and correlated…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
For the complete estimation of arbitrary unknown quantum states by measurements, the use of mutually unbiased bases has been well-established in theory and experiment for the past 20 years. However, most constructions of these bases make…
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum…
We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that…
Classifying locally equivalent graph states, and stabilizer states more broadly, is a significant problem in the theories of quantum information and multipartite entanglement. A special focus is given to those graph states for which…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
In the past decade, remarkable progress has been achieved in deep learning related systems and applications. In the post Moore's Law era, however, the limit of semiconductor fabrication technology along with the increasing data size have…
$k$-Uniform states are fundamental to quantum information and computing, with applications in multipartite entanglement and quantum error-correcting codes (QECCs). Prior work has primarily focused on constructing exact $k$-uniform states or…