Sumesh. K

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 semigroups and dilations, as well as the representations of C*-algebras and Hilbert C*-modules. 

12. C*-extreme points of unital completely positive maps on real C*-algebras, 

(Joinlty with Anand O. R and Arindam Sutradhar) Submitted to journal, arXiv 2025. 

11. What is a Gaussian channel, and when is it physically implementable using a multiport interferometer? 

(Jointly with Repana Devendra and Tiju Cherian John)

    Accepted for publication in Philosophical Transactions of the Royal Society A, arXiv 2025.

10. Generalized C*-convexity in completely positive maps  (Jointly with Anand O. R)

      Journal of Mathematical Analysis and Applications, Volume 551, Issue 2, Part 2 (2025), 23 pages, arXiv.

9. Degradable strong entanglement breaking maps (Jointly with Repana Devendra and Gunjan Sapra)

Linear Algebra and its Applications, 703 (2024), 302–328, arXiv.

8. C*-extreme points of entanglement breaking maps  (Jointly with B. V. Rajarama Bhat, Repana Devendra and Nirupama Mallick)

Rev. Math. Phy. 35 (2023), no. 3, 17 pp, arXiv. 

7. Mapping cone of k-Entanglement Breaking Maps (Jointly with Repana Devendra and Nirupama Mallick)

Positivity 27 (2023), no 1, 32 pp, arXiv.  

6. On a generalization of Ando's dilation theorem (Jointly with Nirupama Mallick)

    Acta Sci. Math. (Szeged)  86 (2020), 273-286, arXiv.

5. Regular representations of completely bounded maps (Jointly with B.V. Rajarama Bhat and Nirupama Mallick)

    Pacific Journal of Mathematics, Vol. 289 (2017), No. 2, 257 - 286.

4. On a tensor-analogue of the Schur product (Jointly with V. S. Sunder)

    Positivity, Volume 20, September 2016, Issue 3, pp 621 - 624, arXiv.

3. CP-H-Extendable Maps between Hilbert modules and CPH- Semigroups (Jointly with Michael Skeide)

    Journal of Mathematical Analysis and Applications, Vol. 414, No. 2 (2014), 886 - 913, arXiv.

2. Bures Distance For Completely Positive Maps (Jointly with B. V. Rajarama Bhat)

    Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 16, No. 4 (2013), arXiv.

1. Stinespring's theorem for maps on Hilbert C*-modules (Jointly with B. V. Rajarama Bhat and G. Ramesh) 

    Journal of Operator Theory 68 (2012), No.1, 173-178, arXiv.

• Generalized C*-convexity in completely positive maps, Conference on Operator Algebra and Related Topics-2025, IIT Bombay, India, February 24-28, 2025.

• On a generalization of Ando's dilation, Recent Advances in Operator Theory and Operator Algebras, ISI Bangalore, India, December 13-19, 2018.

• A generalization of Ando's dilation, SHK Fest- Workshop and Conference on Analysis and Applications, IIT Madras, India, June 18 - 22, 2018.

• Regular representations of completely bounded maps, Conference on Functional Analysis, IIT Bombay, India, October 12 - 15, 2017.

• Regular representations of completely bounded maps, 37th International Conference on Quantum Probability and Related Topics, International Islamic University Malaysia, August 22 - 26, 2016.

• Bures Distance For Completely Positive Maps, Recent Advances in Operator Theory and Operator Algebras, Indian Statistical Institute Bangalore, India, December 31, 2012 - January 11, 2013.

• Gaussian states: A mathematical introduction, Research Workshop on Symplectic Spectral Theory \& Quantum Channels, CUSAT Kerala, India,  May 07-09, 2025. 

• Introduction to Gaussian states and channels, Third National Seminar on Glimpses of Analysis and Geometry (NSGAG 2025), Department of Mathematics, Calicut University, Kerala, India, March 13-14, 2025. (Online) 

• An introduction to separability and entanglement breaking channels, Centre for Data Science, ITER Siksha `O' Anusandhan (Deemed to be University), Odisha, India, September 17, 2022 (Online).

• \textit{Separable and entangled states}, Berchmans Lecture Series in Mathematics, St Berchmans College, Kottayam, Kerala, India, January 16-17, 2020.

• Complex Analysis, Training Programme in Mathematics (TPM), NISER Bhubaneswar, June 04-16, 2018.

• Functional Analysis, Annual Foundation School (AFS)-II, KSOM Kozhikode, June 06 - July 01, 2016.

• Spectral theorem for normal matrices (operators), National Seminar on Spectral theory, BJM Govt College, Chavara, Kerala, India, January 28, 2015.

• Spectral theorem for normal matrices (operators), National Seminar on Analysis and PDE, PTM Govt College, Perinthalmanna, Kerala, India, September 29-30, 2014.