Effect of measurements on quantum speed limit

¹ Quantum Information and Computation Group, Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute - Chhatnag Road, Jhunsi, Prayagraj 211019, India
² Centre for Quantum Science and Technology (CQST), International Institute of Information Technology Hyderabad 500032, India

Received: 12 April 2024
Accepted: 11 June 2024

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 Schrödinger-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.