Department of Mathematics | Indian Institute Of Technology Madras , Chennai

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Sumesh K

Assistant Professor

044 - [22]-57 [46]-42

sumeshkpl

KCB 632

Operator Algebra, Operator Theory, Quantum Information theory.

to email  add  username@iitm.ac.in'

I currently hold the position of Assistant Professor and have been a member of this department since August 2016.

My research lies broadly in Functional Analysis, with particular emphasis on Operator Algebras, Quantum Probability, and Quantum Information Theory. I focus on the theory of completely positive maps and their wide-ranging applications in both operator algebras and quantum information theory.

Currently, I am particularly interested in quantum Gaussian channels and entanglement-breaking channels, which play a central role in understanding quantum communication and the impact of noise on quantum systems. Previously, my work has explored the theory and structure of completely positive and completely bounded maps, their dilations, as well as the representations of C*-algebras and Hilbert C*-modules.

Previous Courses

  • 2025 Jul-Nov: Analysis (MA7840)

  • 2025 Jan-May: Linear Algebra via Matrices (MA2101)

  1. Generalized C*-convexity in completely positive maps

    Author: Anand O. R and K. Sumesh

    Journal: J. Math. Anal. Appl.

    Volume: 551

    Page: 23 pages

    DOI: 10.1016/j.jmaa.2025.129700

    Year: 2025

  2. Degradable strong entanglement breaking maps

    Author: Repana Devendra, Gunjan Sapra and K. Sumesh

    Journal: Linear Algebra Appl.

    Volume: 703

    Page: 302--328 (27 p)

    DOI: 10.1016/j.laa.2024.09.006

    Year: 2024

  3. C*-extreme points of entanglement breaking maps

    Author: B. V. Rajarama Bhat, Repana Devendra, Nirupama Mallick, K. Sumesh

    Journal: Rev. Math. Phys.

    Volume: 35

    Page: 17 p

    DOI: 10.1142/S0129055X23500058

    Year: 2023

  4. Mapping cone of k-entanglement breaking maps

    Author: Repana Devendra, Nirupama Mallick, K. Sumesh

    Journal: Positivity

    Volume: 27

    Page: 32 p

    DOI: 10.1007/s11117-022-00956-4

    Year: 2023

  5. On a generalization of Ando's dilation theorem

    Author: Nirupama Mallick and K. Sumesh

    Journal: Acta Sci. Math. (Szeged)

    Volume: 86

    Page: 273-286 (14 p)

    DOI: 10.14232/actasm-019-775-2

    Year: 2020

  6. Regular representations of completely bounded maps

    Author: B. V. Rajarama Bhat and Nirupama Mallick and K. Sumesh

    Journal: Pacific J. Math.

    Volume: 289

    Page: 257-286 (30 p)

    DOI: 10.2140/pjm.2017.289.257

    Year: 2017

  7. On a tensor-analogue of the Schur product

    Author: K. Sumesh and V. S. Sunder

    Journal: Positivity

    Volume: 20

    Page: 621-624 (4 p)

    DOI: 10.1007/s11117-015-0377-x

    Year: 2016

  8. CP-H-extendable maps between Hilbert modules and CPH-semigroups

    Author: Michael Skeide and K. Sumesh

    Journal: J. Math. Anal. Appl.

    Volume: 414

    Page: 886-913

    DOI: 10.1016/j.jmaa.2014.01.024

    Year: 2014

  9. Bures distance for completely positive maps

    Author: B. V. Rajarama Bhat and K. Sumesh.

    Journal: Infin. Dimens. Anal. Quantum Probab. Relat. Top.

    Volume: 16

    Page: 1350031, 22

    DOI: 10.1142/S0219025713500318

    Year: 2013

  10. Stinespring's theorem for maps on Hilbert C*-modules

    Author: B. V. Rajarama Bhat and G. Ramesh and K. Sumesh

    Journal: J. Operator Theory

    Volume: 68

    Page: 173-178 (6 p)

    DOI: 2012-068-001-009

    Year: 2012

Postdocs:
~ Dr. Arnidam Sutradhar : May 2024 -- Present
~ Dr. Gunjan Sapra : Jul 2021 -- Sep 2023

MSc Project Students:
~ Monideepa Bhatacharjee : Topological vector spaces and convexity structure, 2024.
~ Samiksha Lonkar. : Probability measures on metric spaces, 2024.
~ Tanmay Karmakar : Spectral measures, 2023.
~ Deokar Onkar : Completely positive maps, 2018.