Related papers: Multipartite $d-$level GHZ bases associated with g…
Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a…
We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class…
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…
We find that the m-separability and k-partite entanglement of a multipartite quantum system is correlated with quantum coherence of the same with respect to complete orthonormal bases, distinguishable under local operations and classical…
We propose a protocol for the preparation of generalized Greenberger-Horne-Zeilinger (GHZ) states of $N$ atoms each with $d=3$ or $4$ internal levels. We generalize the celebrated one-axis twisting (OAT) Hamiltonian for $N$ qubits to qudits…
Maximal entangled states (MES) provide a basis to 2d-dimensional particles Hilbert space, d=prime $\ne2$. These states allow generalization of the Mean King Problem. The states may be viewed as build of points each underpins a product state…
The monogamy of entanglement stands as an indispensable feature within multipartite quantum systems. We study monogamy relations with respect to any partitions for the generalized $W$-class (GW) states based on the unified-($q,s$)…
We present a general theory of braided quantum groups in the C*-algebraic framework using the language of multiplicative unitaries. Starting with a manageable multiplicative unitary in the representation category of the quantum codouble 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…
Greenberger-Horne-Zeilinger (GHZ) states, also known as two-component Schr\"{o}dinger cats, play vital roles in the foundation of quantum physics and, more attractively, in future quantum technologies such as fault-tolerant quantum…
Associated to each subset $J$ of the nodes $I$ of a Dynkin diagram is a triangular decomposition of the corresponding Lie algebra $\mathfrak{g}$ into three subalgebras $\widetilde{\mathfrak{g}_{J}}$ (generated by $e_{j}$, $f_{j}$ for $j\in…
Entanglement of qudit pairs, with single particle Hilbert space dimension $d$, has important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. For a pair of qudits of…
Interactions in Many-body systems are typically short-range and few-body. We investigate how such local interactions build up long-range and intrinsically multipartite entanglement by studying the $n$-partite Greenberger-Horne-Zeilinger…
We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and…
We solve stationarity equations of the geometric measure of entanglement for multi-qubit W-type states. In this way we compute analytically the maximal overlap of one-parameter $n$-qubit and two-parameter four-qubit W-type states and their…
We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy…
We show that the standard approach to characterize collective entanglement via genuine multiparty entanglement (GME) leads to an area law in ground and thermal Gibbs states of local Hamiltonians. To capture the truly collective part one…
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum…