Searcharxiv⌕ Search

arXiv subjects

Supriyo Dutta

Publications and source records attributed to Supriyo Dutta.

35 records · Page 2Linked to original sources
arXiv2022

On log-sum inequalities

In information theory, the well-known log-sum inequality is a fundamental tool which indicates the non-negativity for the relative entropy. In this article, we establish a set of inequalities which are similar to the log-sum inequality involving two functions defined on scalars. The parametric extended log-sum inequalities are shown. We extend these inequalities for the commutative matrices. In addition, utilizing the Löwner partial order relation and the Hansen-Pedersen theory for non-commutative positive semi-definite matrices we demonstrate a number of matrix-inequalities analogous to the log-sum inequality.

math.FA↗
arXiv2022

Convex inequalities and their applications to relative operator entropies

A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex functions. As their consequences, we derive the refinements for Young's inequality and Jensen's inequality. In addition, the operator Jensen's type inequality is also developed for conditioned two functions. Utilizing these new inequalities, we investigate the operator inequalities related to the relative operator entropy.

math.CA↗
arXiv2020

Perfect state transfer on hypercubes and its implementation using superconducting qubits

We propose a protocol for perfect state transfer between any pair of vertices in a hypercube. Given a pair of distinct vertices in the hypercube we determine a sub-hypercube that contains the pair of vertices as antipodal vertices. Then a switching process is introduced for determining the sub-hypercube of a memory enhanced hypercube that facilitates perfect state transfer between the desired pair of vertices. Furthermore, we propose a physical architecture for the pretty good state transfer implementation of our switching protocol with fidelity arbitrary close to unity, using superconducting transmon qubits with tunable couplings. The switching is realised by the control over the effective coupling between the qubits resulting from the effect of ancilla qubit couplers for the graph edges. We also report an error bound on the fidelity of state transfer due to faulty implementation of our protocol.

quant-ph↗
arXiv2020

Phase Squeezing of Quantum Hypergraph States

Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $|G\rangle = \frac{1}{\sqrt{2^d}}\sum_{n = 0}^{2^d - 1} (-1)^{f(n)} |n \rangle$, where $f$ is a $d$-variable Boolean function depending on the hypergraph $G$, and $|n \rangle$ denotes a binary vector of length $2^d$ with $1$ at $n$-th position for $n = 0, 1, \dots (2^d - 1)$. The non-classical properties of these states are studied. We consider annihilation and creation operator on the Hilbert space of dimension $2^d$ acting on the number states $\{|n \rangle: n = 0, 1, \dots (2^d - 1)\}$. The Hermitian number and phase operators, in finite dimensions, are constructed. The number-phase uncertainty for these states leads to the idea of phase squeezing. We establish that these states are squeezed in the phase quadrature only and satisfy the Agarwal-Tara criterion for non-classicality, which only depends on the number of vertices of the hypergraphs. We also point out that coherence is observed in the phase quadrature.

quant-ph↗
arXiv2020

A System of Billiard and Its Application to Information-Theoretic Entropy

In this article, we define an information-theoretic entropy based on the Ihara zeta function of a graph which is called the Ihara entropy. A dynamical system consists of a billiard ball and a set of reflectors correspond to a combinatorial graph. The reflectors are represented by the vertices of the graph. Movement of the billiard ball between two reflectors is represented by the edges. The prime cycles of this graph generate the bi-infinite sequences of the corresponding symbolic dynamical system. The number of different prime cycles of a given length can be expressed in terms of the adjacency matrix of the oriented line graph. It also constructs the formal power series expansion of Ihara zeta function. Therefore, the Ihara entropy has a deep connection with the dynamical system of billiards. As an information-theoretic entropy, it fulfils the generalized Shannon-Khinchin axioms. It is a weakly decomposable entropy whose composition law is given by the Lazard formal group law.

math-ph↗
arXiv2019

Ihara Zeta Entropy

In this article, we introduce an entropy based on the formal power series expansion of the Ihara Zeta function. We find a number of inequalities based on the values of the Ihara zeta function. These new entropies are applicable in symbolic dynamics and the dynamics of billiards.

math-ph↗
arXiv2019

Sharma-Mittal Quantum Discord

We demonstrate a generalization of quantum discord using a generalized definition of von-Neumann entropy, which is Sharma-Mittal entropy; and the new definition of discord is called Sharma-Mittal quantum discord. Its analytic expressions are worked out for two qubit quantum states as well as Werner, isotropic, and pointer states as special cases. The R{é}nyi, Tsallis, and von-Neumann entropy based quantum discords can be expressed as limiting cases for of Sharma-Mittal quantum discord. We also numerically compare all these discords and entanglement negativity.

quant-ph↗
arXiv2019

Condition for zero and non-zero discord in graph Laplacian quantum states

This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that every combinatorial graph corresponds to quantum states whose characteristics are reflected in the structure of the underlined graph. A number of combinatorial relations between quantum discord and simple graphs were studied. To extend the scope of these studies, we need to generalize the earlier concepts applicable to simple graphs to weighted graphs, corresponding to a diverse class of quantum states. To this effect, we determine the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and call them graph Laplacian quantum states. We find the graph-theoretic conditions for zero and non-zero quantum discord for these states. We apply these results on some important pure two qubit states, as well as a number of mixed quantum states, such as the Werner, Isotropic, and $X$-states. We also consider graph Laplacian states corresponding to simple graphs as a special case.

quant-ph↗
arXiv2019

From Sharma-Mittal to von-Neumann Entropy of a Graph

In this article, we introduce the Sharma-Mittal entropy of a graph, which is a generalization of the existing idea of the von-Neumann entropy. The well-known R{é}nyi, Thallis, and von-Neumann entropies can be expressed as limiting cases of Sharma-Mittal entropy. We have explicitly calculated them for cycle, path, and complete graphs. Also, we have proposed a number of bounds for these entropies. In addition, we have also discussed the entropy of product graphs, such as Cartesian, Kronecker, Lexicographic, Strong, and Corona products. The change in entropy can also be utilized in the analysis of growing network models (Corona graphs), useful in generating complex networks.

cs.DM↗
arXiv2019

Facets of quantum information under non-Markovian evolution

We consider two non-Markovian models: Random Telegraph Noise (RTN) and non-Markovian dephasing (NMD). The memory in these models is studied from the perspective of quantum Fisher information flow. This is found to be consistent with the other well known witnesses of non-Markovianity. The two noise channels are characterized quantum information theoretically by studying their gate and channel fidelities. Further, the quantum coherence and its balance with mixedness is studied. This helps to put in perspective the role that the two noise channels can play in various facets of quantum information processing and quantum communication.

quant-ph↗
arXiv2018

Constructing Non-isomorphic Signless Laplacian Cospectral Graphs

In this article, we generate large families of non-isomorphic and signless Lalacian cospectral graphs using partial transpose on graphs. Our constructions are significantly powerful. More than $70\%$ of non-isomorphic signless-Laplacian cospectral graphs can be generated with partial transpose when number of vertices is $\le 8$. We have also produced numerous examples of non-isomorphic signless Laplacian cospectral graphs.

math.CO↗
arXiv2018

Construction of cospectral graphs

Construction of non-isomorphic cospectral graphs is a nontrivial problem in spectral graph theory specially for large graphs. In this paper, we establish that graph theoretical partial transpose of a graph is a potential tool to create non-isomorphic cospectral graphs by considering a graph as a clustered graph.

math.CO↗
arXiv2017

Quantum discord of states arising from graphs

Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are reflected in the structure of the corresponding graph. Here, we attempt to develop a graph theoretic study of quantum discord that corresponds to a necessary and sufficient condition of zero quantum discord states which says that the blocks of density matrix corresponding to a zero quantum discord state are normal and commute with each other. These blocks have a one to one correspondence with some specific subgraphs of the graph which represents the quantum state. We obtain a number of graph theoretic properties representing normality and commutativity of a set of matrices which are indeed arising from the given graph. Utilizing these properties we define graph theoretic measures for normality and commutativity that results a formulation of graph theoretic quantum discord. We identify classes of quantum states with zero discord using the said formulation.

quant-ph↗
arXiv2016

Seidel switching for weighted multi-digraphs and its quantum perspective

Construction of graphs with equal eigenvalues (co-spectral graphs) is an interesting problem in spectral graph theory. Seidel switching is a well-known method for generating co-spectral graphs. From a matrix theoretic point of view, Seidel switching is a combined action of a number of unitary operations on graphs. Recent works [1] and [2] have shown significant connections between graph and quantum information theories. Corresponding to Laplacian matrices of any graph there are quantum states useful in quantum computing. From this point of view, graph theoretical problems are meaningful in the context of quantum information. This work describes Seidel switching from a quantum perspective. Here, we generalize Seidel switching to weighted directed graphs. We use it to construct graphs with equal Laplacian and signless Laplacian spectra and consider density matrices corresponding to them. Hence Seidel switching is a technique to generate cospectral density matrices. Next, we show that all the unitary operators used in Seidel switching are global unitary operators. Global unitary operators can be used to generate entanglement, a benchmark phenomena in quantum information processing.

math.CO↗
arXiv2016

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

quant-ph↗
arXiv2016

Bipartite separability and non-local quantum operations on graphs

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 $m \times n$ 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.

quant-ph↗