  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.

Quantum Physics