Entanglement detection with bounded reference frames

TL;DR

This paper investigates how finite-sized quantum reference frames affect the ability to detect entanglement, revealing that larger reference frames are necessary for macroscopic systems to violate local realism.

Contribution

It introduces a framework using spin coherent states as bounded reference frames and determines the minimal size needed to observe violations of local realism.

Findings

Small reference frames suffice for entanglement detection in microscopic systems.

Macroscopic entangled spins require quadratically larger reference frames.

Limited reference frames may explain why violations of local realism are not observed in everyday life.

Abstract

Quantum experiments usually assume the existence of perfect, classical, reference frames, which allow for the specification of measurement settings (e.g. orientation of the Stern Gerlach magnet in spin measurements) with arbitrary precision. If the reference frames are "bounded" (i.e. quantum systems themselves, having a finite number of degrees of freedom), only limited precision can be attained. Using spin coherent states as bounded reference frames we have found their minimal size needed to violate local realism for entangled spin systems. For composite systems of spin-1/2 particles reference frames of very small size are sufficient for the violation; however, to see this violation for macroscopic entangled spins, the size of the reference frame must be at least quadratically larger than that of the spins. Unavailability of such reference frames gives a possible explanation for the non-observance of violation of local realism in everyday experience.