Hi all,
Tomorrow our Jan Seyfried will tell us about his master thesis entitled "Towards efficient testing for zero conditional mutual information ". See below for the abstract. The talk will take place at 2pm in HIT E 41.1
Best, Ladina
*** Title: Towards efficient testing for zero conditional mutual information
Abstract: In quantum learning theory, we aim to extract specific information from a state ρ using measurements on samples of ρ. It is natural to ask what the most sample efficient way to do so is. In this project, we studied the problem of determining whether the conditional mutual information of a tripartite quantum state (or of a classical probability distribution) is either zero or above a certain threshold. This decision problem is interesting because states with zero conditional mutual information are known to have a special structure, which results in interesting properties such as perfect recoverability from the loss of a subsystem under certain constraints. Even classically, the sample complexity of this decision problem is not fully understood, both in terms of achievability and optimality. As part of our work, and as a step towards a sample-efficient quantum algorithm, we present two algorithms with similar sample complexity for the classical regime. Our approaches can serve as an example of how existing algorithms for more general learning tasks can be combined to solve new, more specialized problems. They are also a natural application of robustness bounds and continuity statements, which are of independent interest.