Anoopa Joshi

Bio: Anoopa Joshi is an academic researcher from Indian Institute of Technology, Jodhpur. The author has contributed to research in topics: Quantum entanglement & Laplacian matrix. The author has an hindex of 1, co-authored 2 publications receiving 2 citations.

Concurrence and three-tangle of the graph

Abstract: In this article, we study the entanglement properties of two-qubit quantum states based on concurrence using the graph-theoretic approach. Entanglement properties of a density operator are obtained from the combinatorial Laplacian matrix which is constructed for a given graph. In the study of entanglement, we found that measure of entanglement is either $$ \frac{1}{ |{E}| } $$ or zero for simple graphs. We further propose a simple method to evaluate the three-tangle and analyze inequivalent classes belonging to three-qubit pure states using graph-theoretic perspective. Our results allow a clear distinction between three-qubit separable states, genuinely entangled Greenberger–Horne–Zeilinger and W states, purely based on graphical interpretations.

Chaotic Maps: Applications to Cryptography and Network Generation for the Graph Laplacian Quantum States

Abstract: In this article, we proposed a new chaotic map and is compared with existing chaotic maps such as Logistic map and Tent map. The value of maximal Lyapunov exponent of the proposed chaotic map goes beyond 1 and shows more chaotic behaviour than existing one-dimensional chaotic maps. This shows that proposed chaotic maps are more effective for cryptographic applications. Further, we are using one-dimensional chaotic maps to generate random time series data and define a method to create a network. Lyapunov exponent and entropy of the data are considered to measure the randomness or chaotic behaviour of the time series data. We study the relationship between concurrence (for the two-qubit quantum states) and Lyapunov exponent with respect to initial condition and parameter of the logistic map which is showing how chaos can lead to concurrence based on such Lyapunov exponents.

Some families of density matrices for which separability is easily tested (10 pages)

Abstract: We reconsider density matrices of graphs as defined in quant-ph/0406165. The density matrix of a graph is the combinatorial Laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the ``degree condition'') to test the separability of density matrices of graphs. The condition is directly related to the Peres-Horodecki partial transposition condition. We prove that the degree condition is necessary for separability, and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest-point graphs and perfect matchings. We observe that the degree condition appears to have a value beyond the density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. We isolate a number of problems and delineate further generalizations.

Permutation Symmetric Hypergraph States and Multipartite Quantum Entanglement

Abstract: We demonstrate that a quantum hypergraph state is k-separable if and only if the hypergraph has k-connected components. The permutation symmetric states remains invariant under any permutation. We introduce permutation symmetric states generated by hypergraphs and describe their combinatorial structures. This combinatorial perspective insists us to investigate multi-partite entanglement of permutation symmetric hypergraph states. Using generalised concurrence we measure entanglement up to ten qubits. A number of examples of these states are discussed.