Abstract for the talk on 04.11.2020 (17:00 h)Mathematics of Data Seminar + Felix Klein Colloquium
Stefan Hollands (Leipzig University)
04.11.2020, 17:00 h, Universität Leipzig, Felix-Klein-Hörsaal (Leipzig University)
Physical operations on quantum states mathematically correspond to channels, i.e. completely positive maps. Such operations are typically not invertible. Given that a state having gone through a channel cannot be completely recovered, it is an important question – both theoretically but also for practical purposes such as quantum error correction – under what circumstances the state can perhaps be recovered with a high fidelity, and how. As is well known, channels may only reduce the relative entropy between the given state and some reference state, a fact expressed by the famous "data processing inequality".
In this talk, I present a strengthened version of this inequality for arbitrary channels on v. Neumann algebras and explain how this inequality characterizes the efficiency of state recovery.
(Based on joint work with T. Faulkner.)