Related papers: Condition for zero and non-zero discord in graph L…
Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein \emph{et al.} \emph{Phys. Rev. A,} \textbf{73}:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix…
Correlations may arise in quantum systems through various means, of which the most remarkable one is quantum entanglement. Additionally, there are systems that exhibit non-classical correlations even in the absence of entanglement. Quantum…
Quantum discord has been studied extensively as a measure of non-classical correlations which includes entanglement as a subset. Although it is well known that non-zero discord can exist without entanglement, the origin of quantum discord…
Quantum discord, a key indicator of non-classical correlations in bipartite systems, has been recently extended to multipartite scenarios [Phys. Rev. Lett. 2020, 124:110401]. We present exact analytic formulas for the quantum discord of…
This paper summarizes the basics of the notion of quantum discord and how it relates to other types of correlations in quantum physics. We take the fundamental information theoretic approach and illustrate our exposition with a number of…
We study the phase discrimination problem, in which we want to decide whether the eigenphase $\theta\in(-\pi,\pi]$ of a given eigenstate $|\psi\rangle$ with eigenvalue $e^{i\theta}$ is zero or not, using applications of the unitary $U$…
It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the…
We study the existence of quantum state transfer in $\mathcal{Q}$-graphs in this paper. The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and…
Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. An infinite series of trace formulae is obtained which link together two…
We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate…
The set of Bell-diagonal states for two qubits can be depicted as a tetrahedron in three dimensions. We consider the level surfaces of entanglement and quantum discord for Bell-diagonal states. This provides a complete picture of the…
Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We have generalised the concept of graph states to what we have called mixed graph states, which we define in terms of mixed graphs, that is graphs with both directed and undirected edges, as the density matrix stabilized by the associated…
Quantum discord is significant in analyzing quantum nonclassicality beyond the paradigm of entanglement. Presently we have explored the effectiveness of global unitary operations in manifesting quantum discord from a general two qubit zero…
Homomorphism indistinguishability is a way of characterising many natural equivalence relations on graphs. Two graphs $G$ and $H$ are called homomorphism indistinguishable over a graph class $\mathcal{F}$ if for each $F \in \mathcal{F}$,…
One-way quantum deficit and quantum discord are two important measures of quantum correlations. We revisit the relationship between them in two-qubit systems. We investigate the conditions that both one-way quantum deficit and quantum…
In research concerning quantum networks, it is often assumed that the parties can classically communicate with each other. However, classical communication might introduce a substantial delay to the network, especially if it is large. As…
We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…