SIC-POVMs and MUBs: Sets of Quantum States with Special Properties
- 講者Markus GRASSL 博士 (Max-Planck-Institut für die Physik des Lichts, Erlangen, Germany)
邀請人：鐘楷閔 - 時間2016-09-06 (Tue.) 10:00 ~ 12:00
- 地點資訊所新館107演講廳
摘要
In the talk, I will consider the problem of finding particular sets of quantum states which play a role, for example, in quantum state tomography as well as quantum cryptography. While the problems have a simple mathematical description, they appear to be rather hard to be solved.
So-called SIC-POVMs correspond to maximal sets of equiangular lines in complex space. While we have numerical solutions in dimensions up to
121, algebraic solutions are only known for certain dimensions, and a proof of their (non)existence in all dimensions is elusive.
The second class of states are complete sets of Mutually Unbiased Bases (MUBs) for which we know how to construct them in prime power
dimensions, but in general we only have a lower bound of three bases for arbitrary oddly even dimensions.
More recently, the concept of unextendible MUBs has been introduced, which comes in different flavours. Constructions of such unextndible
sets of MUBs with connections to finite geometry will be presented.
BIO
Markus GRASSL received his diploma degree in Computer Science in 1994 and his doctoral degree in 2001, both from the Fakultät für
Informatik, Universität Karlsruhe (TH), Germany. His dissertation was on constructive and algorithmic aspects of quantum error-correcting
codes. From 1994 to 2007 he was a member of the Institut für Algorithmen und Kognitive Systeme, Fakultät für Informatik, Universität Karlsruhe (TH), Germany. From 2007 to 2008 he was with the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences in Innsbruck. From 2009 to 2014, he was a Senior Research Fellow at the Centre for Quantum Technologies at the National University of Singapore. In 2014, Markus Grassl joined the Institute of Optics, Information and Photonics at the Universität Erlangen-Nürnberg and the Max Planck Institute for the Science of Light (MPL). Currently, he is co-group-leader at MPL.
His research interests include quantum computation, focusing on quantum error-correcting codes, and methods of computer algebra in algebraic coding theory. He maintains tables of good block quantum error-correcting codes as well as good linear block codes.
http://www.markus-grassl.de/