Abstract for the talk on 04.11.2020 (17:00 h)

Mathematics of Data Seminar + Felix Klein Colloquium

Stefan Hollands (Leipzig University)
State recovery
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.)

In reaction to the current Corona threat, physical attendance to this seminar is restricted to 40 participants. Currently, we only allow members from MPI MiS or Leipzig University.
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19.10.2020, 10:20