Unitary-equivariant and permutation-invariant quantum channels

PhD defence by Elias David Michael Theil

Assessment Committee

Associate Professor Albert H. Werner, Department of Mathematical Sciences, University of Copenhagen (Chairperson)
Professor of Quantum Information Theory Michael Walter, Ludwig Maximilian University of Munich
Professor of Quantum Algorithms Zoltán Zimborás, University of Helsinki

Supervisors

Associate Professor Laura Mancinska

Department

Department of Mathematical Sciences

Place

The defence is conducted as a hybrid defence.

To attend the defence in person:
Building: NEXS, Room: Store Auditorium,
Nørre Allé 53, 2200 København N

To attend the defence online:
Please follow the link to attend the defence online: https://ucph-ku.zoom.us/j/8493970969?pwd=MlNwcGZRaFlKUmFjekNHZFdHU09HUT09
Password, if relevant: 586111

Email address to gain access to the thesis: edmt@math.ku.dk.
You will either receive a copy of the thesis or be informed where you can read a physical copy.
Recipients of copies of the thesis are not allowed to share or distribute it due to copyright compliance.

Short description of the thesis

In this thesis I study quantum channels with unitary and permutation symmetries, their classification, implementation, and their performance for specific quantum information tasks. These channels are quantum analogons of important classical algorithms like majority vote or copying information. I give a mathematical classification of these channels via their extremal points, and I provide an efficient implementation for important cases such as purity amplification and cloning. In addition, I give an in-depth analysis of the special case of purity amplification, with the asymptotic behavior of the optimal fidelity, and almost matching non-asymptotic lower bounds. Finally, I use this result for purity amplification to prove an advantage for quantum memory over classical memory for the task of purity amplification.