EPSRC Reference: 
EP/D058643/1 
Title: 
Dilations of Higher Rank Operator Tuples 
Principal Investigator: 
Zacharias, Dr JPH 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Sch of Mathematical Sciences 
Organisation: 
University of Nottingham 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 August 2006 
Ends: 
31 July 2007 
Value (£): 
48,471

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
There has been a tremendous development of operator and operator algebra theory in the past three decades. Both areas have strong connections to quantum theory and form the mathematical backbone of the rapidly developing theory of quantum information. In this theory information is passed on through quantum channels which can be described by mathematical objects called operator tuples. These are objects studied in operator and operator algebra theory. Dilation theory is a very powerful tool to analyze operator tuples. Up to now only single channels have been investigated i.e. single tuples. In this project we want to consider a new type of operator tuple (higher rank tuples) which in quantum information theory corresponds to several independent quantum channels and develop a dilation theory for such tuples. To this end we can make use of the powerful theory of higher rank graph algebras recently developed. Besides these applications our results would also be of interest in abstract operator and operator algebra theory.

Key Findings 
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Organisation Website: 
http://www.nottingham.ac.uk 