22 research outputs found
Reichenbach's Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom
In the paper it will be shown that Reichenbach's Weak Common Cause Principle
is not valid in algebraic quantum field theory with locally finite degrees of
freedom in general. Namely, for any pair of projections A and B supported in
spacelike separated double cones O(a) and O(b), respectively, a correlating
state can be given for which there is no nontrivial common cause (system)
located in the union of the backward light cones of O(a) and O(b) and commuting
with the both A and B. Since noncommuting common cause solutions are presented
in these states the abandonment of commutativity can modulate this result:
noncommutative Common Cause Principles might survive in these models
On the extension of stringlike localised sectors in 2+1 dimensions
In the framework of algebraic quantum field theory, we study the category
\Delta_BF^A of stringlike localised representations of a net of observables O
\mapsto A(O) in three dimensions. It is shown that compactly localised (DHR)
representations give rise to a non-trivial centre of \Delta_BF^A with respect
to the braiding. This implies that \Delta_BF^A cannot be modular when
non-trival DHR sectors exist. Modular tensor categories, however, are important
for topological quantum computing. For this reason, we discuss a method to
remove this obstruction to modularity.
Indeed, the obstruction can be removed by passing from the observable net
A(O) to the Doplicher-Roberts field net F(O). It is then shown that sectors of
A can be extended to sectors of the field net that commute with the action of
the corresponding symmetry group. Moreover, all such sectors are extensions of
sectors of A. Finally, the category \Delta_BF^F of sectors of F is studied by
investigating the relation with the categorical crossed product of \Delta_BF^A
by the subcategory of DHR representations. Under appropriate conditions, this
completely determines the category \Delta_BF^F.Comment: 36 pages, 1 eps figure; v2: appendix added, minor corrections and
clarification
Noncommutative causality in algebraic quantum field theory
In the paper it will be argued that embracing noncommuting common causes in the causal explanation of quantum correlations in algebraic quantum field theory has the following two beneficial consequences: it helps (i) to maintain the validity of Reichenbach's Common Causal Principle and (ii) to provide a local common causal explanation for a set of correlations violating the Bell inequality
Kitaev's quantum double model from a local quantum physics point of view
A prominent example of a topologically ordered system is Kitaev's quantum
double model for finite groups (which in particular
includes , the toric code). We will look at these models from
the point of view of local quantum physics. In particular, we will review how
in the abelian case, one can do a Doplicher-Haag-Roberts analysis to study the
different superselection sectors of the model. In this way one finds that the
charges are in one-to-one correspondence with the representations of
, and that they are in fact anyons. Interchanging two of such
anyons gives a non-trivial phase, not just a possible sign change. The case of
non-abelian groups is more complicated. We outline how one could use
amplimorphisms, that is, morphisms to study the superselection
structure in that case. Finally, we give a brief overview of applications of
topologically ordered systems to the field of quantum computation.Comment: Chapter contributed to R. Brunetti, C. Dappiaggi, K. Fredenhagen, J.
Yngvason (eds), Advances in Algebraic Quantum Field Theory (Springer 2015).
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