Non-Commutative Blahut-Arimoto Algorithms

26/06/2019 @ 11:00 AM – 12:00 PM Asia/Singapore Timezone
Physics conference room, S11-02-07

Speaker: Mr Navneeth Ramakrishnan
Affiliation: NUS / Imperial College London
Host: Dr Derek Ho (on behalf of Assoc Prof Shaffique Adam)

Abstract Details: We generalize alternating optimization algorithms of Blahut-Arimoto type to classical-quantum and fully quantum problems. In particular, we give iterative algorithms to compute the classical capacity of classical-quantum channels and the thermodynamic capacity of quantum channels. The latter includes as special cases the minimal entropy gain of quantum channels and the completely bounded minimal conditional entropy. Our convergence analysis is based on quantum entropy inequalities and leads to an additive approximation error. The number of iterations required to achieve this accuracy is expressed in terms of the relative entropy contraction coefficient of the channel and the input dimension of the channel. We also discuss accelerated heuristics that converge much faster in practice.

About the Speaker: Navneeth did his undergraduate and master's degrees at the National University of Singapore and is currently a PhD student in the group of Mario Berta at Imperial College London. His current research is on convex optimization techniques applied to quantum Shannon theory.