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EPSRC Reference: EP/D058643/1
Title: Dilations of Higher Rank Operator Tuples
Principal Investigator: Zacharias, Dr JPH
Other Investigators:
Researcher Co-Investigators:
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Department: Sch of Mathematical Sciences
Organisation: University of Nottingham
Scheme: Standard Research (Pre-FEC)
Starts: 01 August 2006 Ends: 31 July 2007 Value (£): 48,471
EPSRC Research Topic Classifications:
Mathematical Analysis
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.
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Organisation Website: http://www.nottingham.ac.uk