How long does it take to implement a projective measurement?

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.

Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach

“…Finally, for fundamental criticism about decoherence we refer the reader to Leggett [28], the importance of decoherence for macroscopic objects was discussed in Refs. [29][30][31][32][33][34], and for a general criticism of prevailing notions of classicality in the cosmological context see Ref. [35].…”