Research Projects

Quantum information and computation are two research domains that lie at the intersection of Mathematics, Physics and Computer Science. One of the foremost strategies exercised in these domains is to harness quantum resources which have no classical analogue for information processing and computation. The present project seeks to characterize the completely free operations for quantum conditional entropy. A-unital operations are completely free for quantum conditional entropy, hence their characterization warrants attention. Here we seek to find a decomposition of the A-unital operations and also would like to see whether a revival of a Birkhoff like theorem is possible in the asymptotic case. Further we would also like to probe what can be the possible set of operations which breaks the negativity of quantum conditional entropy. Since quantum conditional entropy can be negative unlike in the classical scenario, this negativity can be counted as an important quantum resource and the operations influencing it call for a mathematical analysis.