New results in quantum-classical covering and classical-quantum packing in network scenarios

I will begin this talk by presenting an overview of the different research themes I pursue. Following this overview, I will describe my results in two of these themes. The first theme focusses on quantum-classical covering wherein I dwell on quantum measurement compression problem (MCP), first formulated and addressed by Winter in
the single measurement scenario. Addressing both one-shot and asymptotic regimes, my work has led to a framework of likelihood POVMs that are proven optimal for a wide array of measurement compression problem involving multiple measurements both in the centralized and distributed scenarios. The likelihood POVMs have also yielded new inner bounds to
the MCP in the distributed one-shot regime. The second theme adresses classical-quantum packing problems and I consider the problem of communicating multiple bit streams over multi-terminal quantum channels. The conventional approach is to employ IID random codes to characterize inner bounds to the CQ capacity of multi-terminal quantum channels.
Building on earlier work for classical channels, I present a new framework of codes possessing algebraic closure properties and derive new inner bounds to the capacity of network CQ channels including the 3-user CQ broadcast and CQ interference channels. Depending on the
availability of time and audience interest, I will brifly talk about a third theme I am currently pursuing. Specifically, I will illustrate my recent ideas on generating distributed entanglement using stabilizer codes over network quantum channels. Time permitting, I will also
briefly present some of my concurrent work on PAC learning from classical-quantum states.