Nonseparability and simultaneous readability

TL;DR

This paper explores quantum nonseparability and introduces the concept of simultaneous readability, analyzing how multiple measurements and post-selection affect the extraction of information from quantum systems.

Contribution

It introduces the concept of simultaneous readability and analyzes the role of nonseparability in quantum measurements involving multiple observables.

Findings

Weak measurement outcomes differ with post-selection.

Nonseparability is crucial in simultaneous measurements.

Different spin components are not simultaneously measurable.

Abstract

In this study, we investigate quantum nonseparability between an observed system and a measuring apparatus, or multiple measuring apparatuses. We show that the physical meaning of the outcome of the measuring apparatus obtained by weak measurement with a post-selection differs critically from that without any post-selection. In this study, the nonseparability plays the essential role, which is shown to be the same in a simultaneous conventional von Neumann-type measurement of multiple observables. From this viewpoint, we suggest a new concept, known as {\it simultaneous readability}, which is the possibility that multiple measuring apparatuses will give the proper information of the observed system simultaneously. Next, we show that different components of the spin of an electron are not simultaneously measurable even if it has EPR correlation with another electron.