Effect of measurements on quantum speed limit

TL;DR

This paper investigates how continuous measurement affects the quantum speed limit, showing that it generally slows down quantum evolution but can enhance speed at small times, with implications for quantum computing and control.

Contribution

It introduces a non-Hermitian Hamiltonian model for continuous measurement and proves that measurement tends to slow quantum evolution, revealing nuanced effects on quantum speed.

Findings

Measurement tends to reduce quantum speed under continuous observation.

At small times, measurement can enhance quantum speed despite finite measurement strength.

The model has potential applications in quantum computing and control.

Abstract

Given the initial and final states of a quantum system, the speed of transportation of state vector in the projective Hilbert space governs the quantum speed limit. Here, we ask the question what happens to the quantum speed limit under continuous measurement process. We model the continuous measurement process by a non-Hermitian Hamiltonian which keeps the evolution of the system Schr{\"o}dinger-like even under the process of measurement. Using this specific measurement model, we prove that under continuous measurement, the speed of transportation of a quantum system tends to zero. Interestingly, we also find that for small time scale, there is an enhancement of quantum speed even if the measurement strength is finite. Our findings can have applications in quantum computing and quantum control where dynamics is governed by both unitary and measurement processes.