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 analyse 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 non-relativistic quantum theory and classical relativistic field theory. (shrink)

We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals for selecting (...) the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the canonical commutation relations. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.

Clifton, Bub, and Halvorson (CBH) have recently argued that quantum theory is characterized by its satisfaction of three fundamental information-theoretic constraints. However, it is not difficult to construct apparent counterexamples to the CBH characterization theorem. In this paper, we discuss the limits of the characterization theorem, and we provide some technical tools for checking whether a theory (specified in terms of the convex structure of its state space) falls within these limits.