Paper detail

How long does it take to implement a projective measurement?

According to the Schrödinger 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.