Quantum observer and Kolmogorov complexity: a model that can be tested

Different observers do not have to agree on how they identify a quantum system. We explore a condition based on algorithmic complexity that allows a system to be described as an objective "element of reality". We also suggest an experimental test of the hypothesis that any system, even much smaller than a human being, can be a quantum mechanical observer.Comment: 11 pages. Section 6 on experimental tests added in version

Renormalized entropy of entanglement in relativistic field theory

Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined unless an ultraviolet cutoff is introduced, but it still diverges in the continuum limit. This behaviour is generic for arbitrary finite-energy states, hence a conceptual tension with the finite entanglement entropy typical of nonrelativistic quantum systems. We introduce a novel approach to explain the transition from infinite to finite entanglement, based on coarse graining the spatial resolution of the detectors measuring the field state. We show that states with a finite number of particles become localized, allowing an identification between a region of space and the nonrelativistic degrees of freedom of the particles therein contained, and that the renormalized entropy of finite-energy states reduces to the entanglement entropy of nonrelativistic quantum mechanics.Comment: 5 pages, 1 figur