Related papers: Entangled graphs: A classification of four-qubit e…
Classification of entanglement is an important problem in Quantum Resource Theory. In this paper we discuss an embedding of this problem in the context of Topological Quantum Field Theories (TQFT). This approach allows classifying…
We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of…
In contrast to abstract statistical analyses in the literature, we present a concrete physical diagrammatic model of entanglement characterization and measure with its underlying discrete phase-space physics. This paper serves as a…
We study entanglement in a system of three coupled quantum harmonic oscillators. Specifically, we use the Schmidt decomposition to analyze how the entanglement is distributed among the three subsystems. The Schmidt decomposition is a…
We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves…
The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
Representing graphs as quantum states is becoming an increasingly important approach to study entanglement of mixed states, alternate to the standard linear algebraic density matrix-based approach of study. In this paper, we propose a…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
We study the entanglement properties of randomized mixed hypergraph states, extending the concept of randomized mixed graph states to encompass hypergraph-based quantum states. In our model, imperfect generalized multi-qubit gates are…
We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the…
Multi-qubit quantum states corresponding to bipartite graphs $G(U,V,E)$ are examined. These states are constructed by applying $CNOT$ gates to an arbitrary separable multi-qubit quantum state. The entanglement distance of the resulting…
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
Graph states are versatile resources for quantum computation and quantum-enhanced measurement. Their generation illustrates a high level of control over entanglement. We report on the generation of continuous-variable graph states of atomic…
We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…
We introduce a protocol to classify three-qubit pure states into different entanglement classes and implement it on an NMR quantum processor. The protocol is designed in such a way that the experiments performed to classify the states can…
The relation between genuine multipartite entanglement in the pure state of a collection of N qubits and the nonclassical correlations in its two-qubit subsystems is studied. Quantum discord is used as the quantifier of nonclassical…
We prove a connection between Schmidt-rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results…
Quantum entanglement, a cornerstone of quantum mechanics, remains challenging to classify, particularly in multipartite systems. Here, we present a new interpretation of entanglement classification by revealing a profound connection to…