Supriyo Dutta (সুপ্রিয় দত্ত)

Research

The area of my research includes the interface of quantum information and graph theory. Ideas from graph theory find a rich breeding ground for investigations into quantum communication and computation. For instance, graph theory builds up a foundation for quantum state transfer, quantum walk, and many other problems related to quantum network. In graph theory, I am interested in constructing cospectral graphs, and characteristics of Ihara zeta functions, and graph machine learning.

Topics: Quantum information theory, Graph theory, Linear algebra and matrix analysis, Entropy, Dynamical system.
Keywords: Graph Laplacian quantum states, Quantum hypergraph states, Quantum entanglement, Quantum discord, Quantum state transfer, Quantum walk, Construction of cospectral graphs, Ihara zeta function, Billiard dynamics, Entropy, Matrix ineuality.

Visualization of quantum states and their properties with combinatorial graphs

A quantum state is represented by a density matrix, which is a positive semidefinite, Hermitian matrix with unit trace. The Laplacian matrices of a combinatorial graph are also a positive semidefinite and Hermitian matrices. Therefore, a normalized Laplacian matrix can be considered as a density matrix of a quantum state. This observation allows us to describe a combinatorial graph as a graphical representation of the quantum state. We investigated different properties of quantum states in terms of graph-theoretic parameters.

4. Condition for zero and nonzero discord in graph Laplacian quantum states. Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee. International Journal of Quantum Information 17 (02), 1950018. arXiv:1705.00808v2.
3. Quantum discord of states arising from graphs. Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee. Quantum Information Processing 16 (8), 183. arXiv:1702.06360v1.
2.Bipartite separability and nonlocal quantum operations on graphs. Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee, R. Srikanth. Physical Review A 94 (1), 012306. arXiv:1601.07704v2.
1. A graph theoretical approach to states and unitary operations. Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee. Quantum Information Processing 15 (5), 2193-2212. arXiv:1502.07821v2.

Quantum hypergraph states and their characteristics

A graph state is a multi-qubit state represented by a graph. The vertices of the graph represent the qubits. We draw an edge between every interacting pair of qubits. Graph states are used in quantum error-correcting codes. They are useful for characterizing computational resources in measurement-based quantum computing. In combinatorics, a hypergraph is a generalization of graphs. A hypergraph consists of vertices and hyperedges. A hyperedge is a set of vertices, that is a generalization of the edges in a graph. In a similar vein, we can generalize graph states to hypergraph states which is also a multi-qubit quantum state associated with a hypergraph. They are essential in different tasks in quantum computing. We investigated quantum entanglement and other quantum correlations for these states.

5. Quantum teleportation of a qutrit state via a hypergraph state in a noisy environment. Souvik Giri, Supriyo Dutta. ArXiv:2409.05675.
4. Quantum Hypergraph States in Noisy Quantum Channels. Supriyo Dutta, Subhashish Banerjee, Monika Rani. Physica Scripta. arXiv:2110.08829. 2023
3. Phase Squeezing of Quantum Hypergraph States. Ramita Sarkar, Supriyo Dutta, Subhashish Banerjee, Prasanta K. Panigrahi. Journal of Physics B: Atomic, Molecular and Optical Physics 54. ArXiv: 2009.01082. 2020.
2. A Boolean Functions Theoretic Approach to Quantum Hypergraph States and Entanglement. Supriyo Dutta. ArXiv:1811.00308. 2018.
1. Permutation Symmetric Hypergraph States and Multipartite Quantum Entanglement. Supriyo Dutta, Ramita Sarkar, Prasanta K Panigrahi. International Journal of Theoretical Physics 58 (11), 3927–3944.

Construction of non-isomorphic cospectral graphs

In spectral graph theory, we represent a graph by a matrix M where M can be the adjacency matrix, Laplacian matrix, signless Laplacian matrix, etc. associated to the graph. Spectra of an M-matrix of a graph is called the M-spectra of the graph. Two isomorphic graphs have equal M-spectra, but the converse is not valid. Constructing large classes of non-isomorphic pairs of graphs with equal M-spectra is an interesting problem in graph theory. We utilized the partial transpose, a prominent tool in quantum information theory, for generating non-isomorphic graphs with equal M-spectra for different M.

2. Constructing Non-isomorphic Signless Laplacian Cospectral Graphs. Supriyo Dutta. Discrete Mathematics 343 (04), 111783. ArXiv:1808.04054.
1. Construction of cospectral graphs. Supriyo Dutta, Bibhas Adhikari. Journal of Algebraic Combinatorics 52, 215–235. 2020. ArXiv:1808.03490.

Information theory and geometry

3. A System of Billiard and Its Application to Information-Theoretic Entropy . Supriyo Dutta, Partha Guha. ArXiv:2004.03444. Accepted in Advances in Theoretical and Mathematical Physics.
2. Ihara Zeta Entropy. Supriyo Dutta, Partha Guha. ArXiv:1906.02514. 2019.
1. A two-parameter entropy and its fundamental properties. Supriyo Dutta, Shigeru Furuichi, Partha Guha. Reviews in Mathematical Physics. 33 (04), 2130003. ArXiv:1908.01696. 2019.

Quantum walk and state transfer

There are different proposals for quantum walk on graphs. The continuous-time quantum walk, the discrete-time quantum walk, the Szegedy quantum walk, and the open quantum walk are a few well-known proposals of quantum walks. All these models are designed on underlined graph structures. The quantum Perfect State Transfer (PST) is an essential tool in quantum communication. Due to interaction between different spin objects state of one spin becomes transferred to another spin. We represent the spins by vertices. When two spin interacts we draw an edge between the corresponding vertices. There is a connection between quantum walk and perfect state transfer. The standard idea of PST is related to continuous time quantum walk. Finding new graphs supporting PST is an interesting problem.

5. Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs. Monika Rani, Supriyo Dutta, Subhashish Banerjee. arXiv:2407.20888.

4. Discrete-Time Open Quantum Walks for Vertex Ranking in Graphs. Supriyo Dutta. ArXiv 2404.14770.

3. Quantum routing in planar graph using perfect state transfer. Supriyo Dutta. Quantum Information Processing. ArXiv:2302.10074.

2. Perfect State Transfer in Arbitrary Distance. Supriyo Dutta. ArXiv:2212.11699. Submitted to Applied Mathematics and Computation.

Perfect state transfer on hypercubes and its implementation using superconducting qubits. Siddhant Singh, Bibhas Adhikari, Supriyo Dutta, David Zueco. Physical Review A 102 (6), 062609.

Miscellaneous

On log-sum inequalities. Supriyo Dutta, Shigeru Furuichi. Linear and Multilinear Algebra. 2023. ArXiv: 2005.03272.
Sharma–Mittal quantum discord. Souma Mazumdar, Supriyo Dutta, Partha Guha. Quantum Information Processing 18 (6), 169. arXiv:1812.00752v2.
Facets of quantum information under non-Markovian evolution. Javid Naikoo, Supriyo Dutta, Subhashish Banerjee. Physical Review A 99 (4), 042128. arXiv:1902.01394v1.
Convex inequalities and their applications to relative operator entropies. Shigeru Furuichi, Hamid Reza Moradi, Supriyo Dutta. Journal of Convex Analysis (Accepted). ArXiv: 2202.04299.

Posters and slides

"On Log-sum Inequalities" was presented physically on 24-th August 2023 at the minisymposium Inequalities and entropy with applications of 10th International Congress on Industrial and Applied Mathematics 2023 Tokyo, organised at Waseda University. Thanks to Prof. Kenjiro YANAGI and Prof. Shigeru FURUICHI for arranging funds to support my travel.
"Constructing cospectral graphs using partial transpose" presented online at "CRM workshop on Graph Theory, Algebraic Combinatorics and Mathematical Physics", organised by The Centre de recherches mathématiques (CRM) of the Université de Montréal on 16-th August 2022. Find the YouTube link for the lecture.
"Elements of Generalized Tsallis Relative Entropy in Classical Information Theory" presented online at Beyond IID in Information Theory 8 , organized by Stanford University on 11.11.2020.
"An Information Theoretic Entropy Related to Ihara ζ Function and Billiard Dynamics" presented online at International Conference on Mathematical Analysis and Applications (MAA 2020) organized by the National Institute of Technology Jamshedpur, on 02.11.2020.
Graph Laplacian Quantum States and Their Properties presented at Centre for Theoretical Studies, Indian Institute of Technology Kharagpur in 2019.
Let’s Measure Randomness: A Glimpse to Generalised Entropies presented at Bose-Fest 2019 organized by the S. N. Bose National Centre for Basic Sciences.
A Boolean Function Theoretic Approach to Quantum Hypergraph States presented at QIPA -2018 organized by the Harish-Chandra Research Institute. December 2 - 8, 2018.
Quantum States: A Pictorial Representation presented at Young Quantum 2017 organized by the Harish-Chandra Research Institute. February 27 - March 1, 2017.

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