Angular momentum conservation in measurements on spin Bose-Einstein condensates

TL;DR

This paper examines a paradox in quantum measurements of spin Bose-Einstein condensates, questioning how angular momentum conservation is maintained during measurements and challenging the idea that apparatus interactions resolve the paradox.

Contribution

It demonstrates that the common explanation involving measurement apparatus interactions does not resolve the angular momentum conservation paradox in spin BEC measurements.

Findings

Standard quantum mechanics predicts large spin angular momentum in distant labs after few measurements.

The proposed solution involving apparatus interaction does not fully resolve the paradox.

Angular momentum conservation may only hold on average, not in individual measurement realizations.

Abstract

We discuss a thought experiment where two operators, Alice and Bob, perform transverse spin measurements on a quantum system; this system is initially in a double Fock spin state, which extends over a large distance in space so that the two operators are far away from each other. Standard quantum mechanics predicts that, when Alice makes a few measurements, a large transverse component of the spin angular momentum may appear in Bob's laboratory. A paradox then arises since local angular momentum conservation seems to be violated. It has been suggested that this angular momentum may be provided by the interaction with the measurement apparatuses. We show that this solution of the paradox is not appropriate, so that another explanation must be sought. The general question is the retroaction of a quantum system onto a measurement apparatus. For instance, when the measured system is entangled with another quantum system, can its reaction on a measurement apparatus be completely changed? Is angular momentum conserved only on average over several measurements, but not during one realization of the experiment?