How long does it take to implement a projective measurement?

TL;DR

This paper estimates the minimum time required for a quantum measurement to occur, showing it scales with the size of the quantum system and confirming the bound with experimental data.

Contribution

It introduces a fundamental lower bound on measurement time based on physical principles and provides a pedagogical explanation of the underlying concepts.

Findings

Measurement time scales with system size (~10^{-5} s/m).

Experimental measurements are consistent with the proposed bound.

The bound is derived using concepts like Lieb-Robinson velocity and quantum speed limit.

Abstract

According to the Schr\"odinger equation, a closed quantum system evolves continuously in time. If it is subject to a measurement however, its state changes randomly and discontinuously, which is mathematically described by the projection postulate. But how long does it take for this discontinuous change to occur? Based on simple estimates, whose validity rests solely on the fact that all fundamental forces in nature are finite-ranged, we show that the implementation of a quantum measurement requires a minimum time. This time scales proportionally with the diameter of the quantum mechanical object, on which the measured observable acts non-trivially, with the proportionality constant being around $10^{-5}$ s/m. We confirm our bound by comparison with experimentally reported measurement times for different platforms. We give a pedagogical exposition of our argumentation introducing along the way modern concepts such as ancilla-based measurements, the quantum speed limit, and Lieb-Robinson velocity bounds.