B V Rajarama Bhat

Specializing in Quantum Probability, Operator Algebras and Quantum Information theory.

Professor, Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore

India.

Research Overview

My research focuses on the following topics :

Quantum Markov Semigroups: Dilation theory and tensor product systems of Hilbert spaces and Hilbert C*-modules.
Quantum Information Theory: Completely Positive maps, quantum channels and their asymptotics.
Operator Algebras: C*-algebras and von Neumann algebras
Matrix theory: Exploring the geometry and fixed points of completely positive, trace-preserving maps.

Jointly with Tirthankar Bhattacharyya. This text serves as both a reference for active researchers and as an advanced guide for graduate students.

A complete characterization of eventually entanglement breaking unital quantum channels
(Joint work with Pankaj Dey and Biswarup Saha). We see that a unital channel is eventually entanglement breaking if and only if all its eigenvectors corresponding to non-zero eigenvalues commute with peripheral eigenvectors.
On regions of mixed unitarity for semigroups of unital quantum channels
(Joint work with Repana Devendra). It is shown that all unital quantum channels are eventually mixed unitary.
Unitary orthonormal bases of finite dimensional inclusions
(Joint work with Keshab Chandra Bakshi). Spectral conditions are obtained for existence or unitary orthonormal bases.

Infinite Dimensional Analysis, Quantum Probability and Related Topics (Managing Editor)
Journal of the Ramanujan Mathematical Society (Editor)
Indian Journal of Pure and Applied Mathematics (Editor)
Annals of Funcitonal Analysis (Editor)

Arghya Chongdar (ISI, Thesis submitted)

Biswarup Saha (ISI)

Astrid Swizell Dias (Matscience)