Entanglement and Open Systems in Algebraic Quantum Field Theory

Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyze entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter’s ability to perform operations on a field in one spacetime region that can disentangle its state from the state of the field in other spacelike-separated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum field theory, and yield a fresh perspective on the ways in which the theory differs conceptually from both standard nonrelativistic quantum theory and classical relativistic field theory. “. . . despite its conservative way of dealing with physical principles, algebraic QFT leads to a radical change of paradigm. Instead of the Newtonian view of a space-time filled with a material content one enters the reality of Leibniz created by relation (in particular inclusions) between ‘monads’ (∼ the hyperfinite type III1 local von Neumann factors A(O) which as single algebras are nearly void of physical meaning)” Schroer (1998, p. 302). ∗Department of Philosophy, 1001 Cathedral of Learning, University of Pittsburgh, Pittsburgh, PA 15260, USA, emails: [email protected], [email protected].