[PAST EVENT] Mathematics Colloquium: Daniel Puzzouli (University of Ottawa and Carleton University)
Title: Entanglement in single-shot quantum channel discrimination and
norms on linear maps of matrices
Abstract: In finite dimensional quantum information, transformations between systems are represented by quantum channels: completely positive and trace preserving linear maps between matrix spaces. Single-shot quantum channel discrimination is the task of determining which of two known channels is acting on a system, given only a single use. We will review how entanglement can be used in this task to gain an advantage, and how this phenomenon is directly connected to properties of norms measuring the distance between the channels. In particular, the advantage provided by entanglement is quantified by the gap between the completely bounded trace norm and the induced trace norm. We will discuss recent results related to these norms and single-shot quantum channel discrimination, as well as open problems.