arXiv subjects

Supriyo Dutta

Publications and source records attributed to Supriyo Dutta.

At least 19 recordsLinked to original sources

arXiv2026

$r$-deformed $\alpha$-$z$-R\'enyi relative entropy

In this article, we consider the $r$-logarithm for defining three-parameter family of R\'{e}nyi relative entropies that are generalization of the $\alpha$-$z$-R\'{e}nyi relative entropies. All the members of $r$-deformed $\alpha$-$z$-R\'{e}nyi relative entropies satisfy the necessary axioms to be a divergence. We expose the range of parameters $\alpha$, $z$ and $r$ for which the data processing inequality holds. We also establish that $r$-deformed $\alpha$-$z$-R\'{e}nyi relative entropy is an upper bound of the Tsallis relative entropy. Now, we have two upper bounds of the Tsallis relative entropy, which are $r$-deformed $\alpha$-$z$-R\'{e}nyi relative entropy and the other one, which is discussed in literature. We investigate the order relationship between these two upper bounds of the Tsallis relative entropy. We observe that our new upper bound is more tighter when applicable to the density operators.

math-ph↗

arXiv2026

Perfect State Transfer on Quotient Graphs in Shunt Decomposition-Based Quantum Walks

This paper investigates perfect state transfer (PST) in discrete-time quantum walks constructed via the shunt decomposition method. The walks are defined on a graph $G$ and its associated quotient graph $G/\pi$, induced by an equitable partition $\pi$. Through the shunt decomposition of $G$, we derive an explicit relation between the shift operator of the parent graph $G$ and that of its quotient graph $G/\pi$. We construct a reflection operator based on the characteristic matrix, which establishes a connection between the transition operator of the parent graph and that of its lower-dimensional quotient graph. We then prove that PST occurs on $G$ if and only if it occurs on $G/\pi$. Furthermore, we express the unitary evolution operator of the quotient graph in terms of Chebyshev polynomials of the first kind, from which we derive explicit criteria for PST. As an application, we establish PST on the cycle graph $C_{n}$ at time $k = n/2$, and lift the result to the parent graph $C_{2n}$ via the equitable partition $\pi$. We further show that if an equitable partition $\pi$ of $G$ induces a quotient isomorphic to $K_n^{\circlearrowleft}$, the complete digraph on $n$ vertices with a loop at every vertex, then PST occurs at step $k = n$, and the walk is periodic at $k = 2n$. This framework is applied to two families of graphs, which are the complete bipartite digraph $K_{n,n}^{\rightleftharpoons}$ and the circulant graph $\operatorname{Circ}(2n, S)$, where $S$ consists of all odd residues modulo $2n$ and $n = 2^s$ for some $s \geq 1$, establishing PST in their respective line digraphs. Collectively, these results also answer the question posed by Godsil and Zhan concerning which shunt decompositions or embeddings of a graph admit PST.

math.CO↗

arXiv2026

Quantum state transfer on a scalable network under unital and non-unital noise

We investigate quantum state transfer on a class of bipartite graphs, namely the butterfly graphs, within the framework of discrete-time quantum walks. These graphs facilitate the construction of scalable quantum networks that enable communication between a sender and a receiver via perfect state transfer. Our analysis demonstrates that state transfer occurs across different butterfly graphs, thereby extending the known families of networks that support high-fidelity quantum state transfer. In addition to the ideal noiseless dynamics, we further investigate the robustness of quantum state transfer in the presence of non-Markovian environmental noise, specifically, random telegraph noise, modified Ornstein-Uhlenbeck noise, which are examples of unital noise and non-Markovian amplitude damping noise, non-unital noise. These noise models capture different types of system-environment interactions and memory effects that influence the coherence of the quantum walk. These findings contribute to the theoretical understanding of how butterfly graph constructions influence quantum transport phenomena.

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arXiv2026

Structural and Spectral Properties of Prime Order Element Graph of Finite Abelian Groups

Given a finite group $G$, the \emph{Prime Order Element (POE) Graph} $\Gamma(G)$ consists of the group elements as the vertices, and two vertices $x$ and $y$ are adjacent if and only if $o(xy)$ is prime. This paper presents a thorough structural and spectral analysis of the POE graphs associated with the finite Abelian groups of different types. The order of a finite Abelian group may be a prime or a product of primes, which influences the structure of POE graphs. The POE graph is connected when the order of the Abelian group is a square-free integer. The POE graphs of the other Abelian groups have multiple connected components. Some of these components are isomorphic to the POE graph of a lower-order group. We study various graph-theoretic properties of the components, including regularity and bipartiteness. Arranging the elements of the group in a number of particular orders, we observe the block structure in the adjacency matrix of POE graphs. It assists us in investigating the spectral properties of POE graphs. We explicitly derive the characteristic polynomials governing both integral and irrational eigenvalues, and compute the eigenvalues with multiplicity in terms of the structure of the graphs.

math.CO↗

arXiv2026

Community detection in network using Szegedy quantum walk

In a network, the vertices with similar characteristics construct communities. The vertices in a community are well-connected. Detecting the communities in a network is a challenging and important problem in the theory of complex networks. One approach to solving this problem uses the classical random walks on graphs. In quantum computing, quantum walks are the quantum mechanical counterparts of classical random walks. In this article, we employ a variant of Szegedy's quantum walk to develop a procedure for discovering the communities in networks. The limiting probability distribution of quantum walks assists us in determining the inclusion of a vertex in a community. We apply our community detection procedure to a variety of graphs and social networks, including the relaxed caveman graph, $l$-partition graph, Karate club graph, and the dolphin's social network, among others.

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arXiv2025

Do quantum linear solvers offer advantage for networks-based system of linear equations?

In this exploratory numerical study, we assess the suitability of Quantum Linear Solvers(QLSs)toward providing a quantum advantage for Networks-based Linear System Problems (NLSPs). NLSPs naturally arise from graphs, and are of importance as they are connected to real-world applications. The achievable advantage with a QLS for an NLSP depends on the interplay between the scaling of condition number and sparsity of matrices associated with the graph family. We analyze 50 graph families and identify that within the scope of our study, only 21 of them exhibit prospects for an exponential advantage with the Harrow-Hassidim-Lloyd (HHL) algorithm relative to an efficient classical solver. We call graph families that offer advantage with HHL as good graph families. We also compare the performance of the considered 50 graph families with 7 other QLSs. Furthermore, we report that some graph families graduate from offering no advantage with HHL to promising an exponential advantage with improved algorithms such as the Childs-Kothari-Somma algorithm. We also introduce a unified graph superfamily and show the existence of infinite good graph families in it. Since the runtime expressions for linear solvers involve condition number, which in itself is not easy to compute, ascertaining advantage prospects with quantum linear solvers itself is not an easy problem. Thus, we conjecture the conditions under which one may visually examine a graph family and guess the prospects for an advantage. Finally, we very briefly touch upon some practical issues that may arise even if the aforementioned graph theoretic requirements are satisfied, including quantum hardware challenges.

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arXiv2025

Quantum state transfer and periodicity in discrete-time quantum walks under non--Markovian dephasing noise

In quantum communication, quantum state transfer from one location to another in a quantum network plays a prominent role, where the impact of noise could be crucial. The idea of state transfer can be fruitfully associated with quantum walk on graphs. We investigate the consequences of non-Markovian quantum noises on periodicity and state transfer induced by a discrete-time quantum walk on graphs, governed by the Grover coin operator. Different bipartite graphs, such as the path graph, cycle graph, star graph, and complete bipartite graph, present periodicity and state transfer in a discrete-time quantum walk depending on the topology of the graph. We investigate the effect of quantum non-Markovian dephasing noises, particularly quantum non-Markovian Random Telegraph Noise (RTN) and modified non-Markovian Ornstein-Uhlenbeck Noise (OUN) on state transfer and periodicity. We demonstrate how the RTN and OUN noises allow state transfer and periodicity for a finite number of steps in a quantum walk. Our investigation brings out the feasibility of state transfer in a noisy environment.

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arXiv2024

Quantum teleportation of a qutrit state via a hypergraph state in a noisy environment

The concept of quantum teleportation is fundamental in the theory of quantum communication. Developing models of quantum teleportation in different physical scenario is a modern trend of research in this direction. This work is at the interface of hypergraph theory and quantum teleportation. We propose a new teleportation protocol for qutrit states in a noisy environment. This protocol utilizes a shared quantum hypergraph state between parties as quantum channels, to carry quantum information. During the preparation of the shared state different quantum noise may act on it. In this article, we consider six types of noises which are generalized for qutrits using Wyel operators. They are the qutrit-flip noise, qutrit-phase-flip noise, depolarizing noise, Markovian and non-Markovian amplitude damping channel, Markovian and non-Markovian dephasing channel, and non-Markovian depolarization noise. There are only five qutrit hypergraph states which satisfies our requirements to be used as a channel. We consider all of them in this work. For different hypergraph states and different noises we work out the analytical expressions of quantum teleportation fidelity.

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arXiv2024

Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs

In this work, we present a new model of the Discrete-Time Open Quantum Walk (DTOQW) applicable to an arbitrary graph, thereby going beyond the case of quantum walks on regular graphs. We study the impact of noise in the dynamics of quantum walk by applying Kraus operators of different dimensions which are constructed using the Weyl operators. The DTOQW employs these Kraus operators as its coin operators. The walker dynamics are studied under the impact of non-Markovian amplitude damping, dephasing and depolarizing noise channels. We also implement the walk on various graphs, including path graphs, cycle graphs, star graphs, complete graphs, complete bipartite graphs, etc. We gauge the dynamics by computing coherence and fidelity at different time steps, taking into account the influence of noise. Furthermore, we compute the probability distribution at different time steps for the above noises, which represents the availability of the quantum walker at different vertices of the graph.

quant-ph↗

arXiv2024

A two-parameter entropy and its fundamental properties

This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized entropy and divergence, for instance, the sub-additive property, strong sub-additive property, joint convexity, and information monotonicity. This article presents an exposit investigation on the information-theoretic and information-geometric characteristics of the new generalized entropy and compare them with the properties of the Tsallis and the Shannon entropy.

math-ph↗

arXiv2024

Discrete-Time Open Quantum Walks for Vertex Ranking in Graphs

This article presents a new quantum PageRank algorithm on graphs using discrete-time open quantum walks. Google's PageRank is a widely used algorithm for ranking the web pages on the World Wide Web in classical computation. From a broader perspective, it is also a fundamental measure for quantifying the importance of vertices in a network. Similarly, the new quantum PageRank also serves to quantify the significance of a network's vertices. In this work, we extend the concept of discrete-time open quantum walk on arbitrary directed and undirected graphs by utilizing the Weyl operators as Kraus operators. This new model of quantum walk is useful for building up the quantum PageRank algorithm, discussed in this article. We compare the classical PageRank and the newly defined quantum PageRank for different types of complex networks, such as the scale-free network, Erd\H{o}s-R\'enyi random network, Watts-Strogatz network, spatial network, Zachary Karate club network, GNC, GN, GNR networks, Barab\'asi and Albert network, etc. In addition, we study the convergence of the quantum PageRank process and its dependency on the damping factor $\alpha$. We observe that this quantum PageRank procedure is faster than many other proposals reported in the literature.

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arXiv2023

Qudit States in Noisy Quantum Channels

In this work, we analyze a number of noisy quantum channels on a family of qudit states. The channels studied are the dit-flip noise, phase flip noise, dit-phase flip noise, depolarizing noise, non-Markovian Amplitude Damping Channel (ADC), dephasing noise, and depolarization noise. To gauge the effect of noise, the fidelity between the original and the final states is studied. The change of coherence under the action of noisy channels is also studied, both analytically and numerically. Our approach is advantageous as it has an explicit relation to the original approach to the multi-qubit hypergraph states.

quant-ph↗

arXiv2023

Quantum routing in planar graph using perfect state transfer

In this article, we consider a spin-spin interaction network governed by $XX + YY$ Hamiltonian. The vertices and edges of the network represent the spin objects and their interactions, respectively. We take a privilege to switch on or off any interaction, that assists us to perform multiple perfect state transfers in a graph simultaneously. We also build up a salable network allowing quantum communication between two arbitrary vertices. Later we utilize the combinatorial characteristics of hypercube graphs to propose a static routing schema to communicate simultaneously between a set of senders and a set of receivers in a planar network. Our construction is new and significantly powerful. We elaborate multiple examples of planar graphs supporting quantum routing where classical routing is not possible.

quant-ph↗

arXiv2022

Perfect state transfer using Markovian quantum walk

The quantum Perfect State Transfer (PST) is a fundamental tool of quantum communication in a network. It is not easy to achieve in practice. The original idea of PST depends on the fundamentals of the continuous-time quantum walk. A path graph with at most three vertices allows PST based on continuous-time quantum walk. Based on the Markovian quantum walk, we introduce a significantly powerful method for PST in this article. We establish PST between the extreme vertices of a path graph of arbitrary length. Moreover, any pair of symmetric vertices in a path graph allows PST under Markovian quantum walks. We extend our investigations for the cycle graphs. The cycle graphs with more than $4$ vertices do not allow the PST based on the continuous-time quantum walk. In contrast, a cycle graph with $2m$ vertices exhibits PST based on Markovian quantum walk between the vertices $j$ and $j + m$ for $j = 0, 1, \dots (m - 1)$, where $m > 0$ is an integer.

quant-ph↗

arXiv2022

A Boolean Functions Theoretic Approach to Quantum Hypergraph States and Entanglement

The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined by a Boolean function. In contrast, we can find a hypergraph, corresponding to a Boolean function. This investigation develops a number of combinatorial structures concerned with the hypergraph states. For instance, the elements of the computational basis generate a lattice. The chains and antichains in this lattice assist us to find the equation of the Boolean function explicitly as well as to find a hypergraph. In addition, we investigate the entanglement property of the hypergraph states in terms of their combinatorial structures. We demonstrate several classes of hypergraphs, such that every cut of equal length on the corresponding hypergraph states has an equal amount of entanglement.

math.CO↗

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.

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