Measurement time of weak measurements on large entangled systems

TL;DR

This paper demonstrates that the collapse of a large, entangled quantum system can be achieved through purely weak measurements, with collapse time scaling as a double logarithm of system size, supporting the idea that weak measurements underpin all physical measurement processes.

Contribution

It shows that the collapse of a many-body entangled wave function can be reproduced using only weak measurements, with a specific scaling law for collapse time.

Findings

Collapse time scales as a double logarithm of the number of qubits.

Weak measurements can reproduce key features of strong measurement outcomes.

Supports the hypothesis that weak measurements form the basis of all physical measurements.

Abstract

It is well established that starting only with strong, projective quantum measurements, experiments can be designed to allow weak measurements, which lead to random walk between the possible final measurement outcomes. However, one can ask the reverse question: starting with only weak measurements, can all the results of standard strong measurements be recovered? Prior work has shown that some results can be, such as the Born rule for the probability of measurement outcomes as a function of wave intensity. In this paper we show that another crucial result can be reproduced by purely weak measurements, namely the collapse of a many-body, nonlocally entangled wave function on a time scale comparable to the characteristic time of a single, local measurement; for an entangled state of a single excitation among $N$ qubits, we find the collapse time scales as a double logarithm of $N$. This result affirms the self-consistency of the hypothesis that spontaneous weak measurements lie at the base of all physical measurements, independent of human observers.