Tues. seminar

[Statphys]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR



Tuesday, 30 March   -   11:00 hrs.



Lecture Room D - SISSA Main Building





Saverio PASCAZIO   (University of Bari)



"Classical statistical mechanics approach to multipartite entanglements"



Abstract



Entanglement is one of the most intriguing features of quantum  
mechanics.  It is widely used in quantum communication and information  
processing and plays a key role in quantum computation.  At the same  
time, entanglement is not fully understood.  It is deeply rooted into  
the linearity of quantum theory and in the superposition principle and  
(for pure states) is essentially and intuitively related to the  
impossibility of factorizing the state of the total system in terms of  
states of its constituents.

The characterization and quantification of entanglement is an open and  
challenging problem. One can give a good definition of bipartite  
entanglement in terms of the von Neumann entropy or the entanglement  
of formation.  The problem of defining multipartite entanglement is  
more difficult and no unique definition exists.

We characterize the multipartite entanglement of a system of  n   
qubits in terms of the distribution function of the bipartite purity  
over balanced bipartitions.  We search for maximally multipartite  
entangled states, whose average purity is minimal, and recast this  
optimization problem into a problem of statistical mechanics, by  
introducing a cost function, a fictitious temperature and a partition  
function.  By investigating the high-temperature expansion, we obtain  
the first three moments of the distribution.  We find that the problem  
exhibits frustration.

We focus on fundamental issues and possible applications.