The University of Queensland
 
 
Centre for Mathematical Physics
 
SEMINAR
 
 
Speaker:  Andrew Doherty, Physics, UQ
 
Title:  Entanglement, positive maps, the deFinetti theorem and all that...
 
 10am, Wednesday 12th October, 2005
 
  Priestley Blding, room 641
 
Abstract:
 
I will describe my recent work with many collaborators on mixed state 

entanglement from a point of view that might be of interest to 

mathematicians. In the physical theory of entanglement there are 

observables, known as entanglement witnesses, that can in principle be 

measured to prove that a state is entangled. When interpreted as 

Hamiltonians these observables have the property that all low energy 
states are entangled. Mathematically these objects correspond both to 
positive linear maps between matrix algebras and to certain kinds of 
positive polynomials. Positive maps were much studied in the seventies 
by mathematicians such as Woronowicz and Choi and it has been known 
for some time that many of their results have direct application in quantum
 information theory. I will describe a further unlikely connection. It turns 
out that a quantum mechanical generalisation of de Finetti's representation 
theorem for exchangeable probability distributions provides both methods
for checking whether quantum states are entangled and an apparently new 
characterization of positive maps in terms of completely positive maps.
 
All interested are invited to attend.

Enquiries to Katrina Hibberd email: keh@maths.uq.edu.au