Some Entanglement Survives Most Measurements

TL;DR

This paper investigates how repeated weak measurements on an entangled quantum system cannot fully eliminate entanglement unless the measurements become perfectly projective, highlighting practical limitations in quantum state preparation.

Contribution

It demonstrates that some entanglement persists after multiple non-projective measurements unless measurements are idealized as perfectly projective, extending understanding of measurement limitations.

Findings

Entanglement remains unless measurements are perfectly projective.

Weak measurements cannot fully disentangle a system from its environment.

Results apply to both n-qubit and n-dimensional states.

Abstract

To prepare quantum states and extract information, it is often assumed that one can perform a perfectly projective measurement. Such measurements can achieve an uncorrelated system and environment state. However, perfectly projective measurements can be difficult or impossible to perform in practice. We investigate the limitations of repeated non-projective measurements in preparing a quantum system. For an $n$-qubit system initially entangled with its environment and subsequently prepared with measurements, using a sequence of weak measurements, we show that some entanglement remains unless one of the measurement operators becomes perfectly projective through an extreme limiting process. Removing initial (unentangled) correlations between a system and its environment and the scenario where measurement outcomes are not tracked are also discussed. We present results for $n$-qubit and $n$-dimensional input states.