On quantum randomness and quantum resources

This thesis is consisted of two independent parts. The first part is on entanglement, quantum randomness, and complexity beyond scrambling. More explicitly, we study the Rényi entanglement entropies of quantum designs. The results lay the mathematical foundation for studying the hierarchy of complexities in between scrambling and Haar randomness by entanglement. The second part explores the general aspects of quantum resource theory. We introduce three theories that do not rely on the specific resource: the theory of resource destroying maps, the one-shot operational resource theory, and the resource theory of quantum channels.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Physics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Liu, Zi-Wen.

Advisor dc:contributor.advisor

• Seth Lloyd.

• Physics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/122846

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/122846