Universiteit Utrecht

Department of Mathematics


Abstract


Multi partite Bell-type inequalities for partial separability and quantum mechanical violations
Michiel Seevinck, February 5, 2003

Multi-partite entangled states are of high interest to the new field of quantum information. For the experimental verification of the existence of such entangled states sufficient and/or necessary conditions are needed. In this talk I will present different types of such conditions and show that violations of certain Bell-type inequalities can act as sufficient conditions for multi-partite entanglement.

Because the Bell-type inequalities which will be considered are derived from certain conditions on local hidden variable theories, they also serve the purpose of telling us something about the relationship between quantum mechanics and local realism. In particular, I will focus on the difference between factorisability in hidden variable theories and separability in quantum mechanics. A key distinction in the multipartite case (as opposed to the well-studied bi-partite case) is the distinction between full and partial factorisability for hidden variable theories and full and partial separability in quantum mechanics.

These distinctions give rise to a new type of Bell-inequalities which apply to hidden variable theories with only partial factorisability. I will use these inequalities to show the remarkable fact that full entanglement is in general not sufficient to violate all Bell-type inequalities. This has some relevance to the foundations of physics because it would imply that some states, despite being fully entangled, could nevertheless have an embedding within partial factorisable local hidden variable theories.


Back to the history of the seminar or the Colloquium Stochastiek homepage.
Martijn Pistorius (pistorius@math.uu.nl)