Bibhas Adhikari

Structured Backward Errors and Pseudospectra of Structured Matrix Pencils

Structured backward perturbation analysis plays an important role in the accuracy assessment of computed eigenelements of structured eigenvalue problems. We undertake a detailed structured backward perturbation analysis of approximate eigenelements of linearly structured matrix pencils. The structures we consider include, for example, symmetric, skew-symmetric, Hermitian, skew-Hermitian, even, odd, palindromic, and Hamiltonian matrix pencils. We also analyze structured backward errors of approximate eigenvalues and structured pseudospectra of structured matrix pencils.

A graph theoretical approach to states and unitary operations

Building upon our previous work, on graphical representation of a quantum state by signless Laplacian matrix, we pose the following question. If a local unitary operation is applied to a quantum state, represented by a signless Laplacian matrix, what would be the corresponding graph and how does one implement local unitary transformations graphically? We answer this question by developing the notion of local unitary equivalent graphs. We illustrate our method by a few, well known, local unitary transformations implemented by single-qubit Pauli and Hadamard gates. We also show how graph switching can be used to implement the action of the

Laplacian matrices of weighted digraphs represented as quantum states

C_\mathrm{NOT}

Structural and spectral properties of corona graphs

CNOT gate, resulting in a graphical description of Bell state generation.

Interpreting nucleation as a network formation process

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 separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension

Quantum discord of states arising from graphs

m \times n

A Parametric Model Approach for Structural Reconstruction of Scale-Free Networks

arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.

Blind signal modulation recognition through clustering analysis of constellation signature

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 general weighted directed graph framework for investigating properties of a large class of quantum states which are defined by three types of Laplacian matrices associated with such graphs. We generalize the standard framework of defining density matrices from simple connected graphs to density matrices using both combinatorial and signless Laplacian matrices associated with weighted directed graphs with complex edge weights and with/without self-loops. We also introduce a new notion of Laplacian matrix, which we call signed Laplacian matrix associated with such graphs. We produce necessary and/or sufficient conditions for such graphs to correspond to pure and mixed quantum states. Using these criteria, we finally determine the graphs whose corresponding density matrices represent entangled pure states which are well known and important for quantum computation applications. We observe that all these entangled pure states share a common combinatorial structure.