Effect of measurements on quantum speed limit

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{ö}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.

7 pages, 3 figures. Comments are welcome

References in corpus (27)

• The maximum speed of dynamical evolution
• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Faster than Hermitian Quantum Mechanics
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Stronger uncertainty relations for the sum of variances
• Energy-time uncertainty relation for driven quantum systems
• Tightening Quantum Speed Limits for Almost All States
• Environment assisted speed-up of the field evolution in cavity QED
• Quantum Coherence Sets The Quantum Speed Limit For Mixed States
• Tight, robust, and feasible quantum speed limits for open dynamics
• Quantum Speed Limit For Mixed States Using Experimentally Realizable Metric
• On the Connection Between Entanglement and the Speed of Quantum Evolution
• Quantum Speed Limit for States with a Bounded Energy Spectrum
• Quantum Speed Limit and Optimal Control of Many-Boson Dynamics
• Quantum speed limits for information and coherence
• Phases of quantum states in completely positive non-unitary evolution
• Quantum Speed Limits for Observables
• Operational definition of a quantum speed limit
• Topological Speed Limit
• Quantum Speed Limits under Continuous Quantum Measurements
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Evolution speed of open quantum dynamics
• Uhlmann's geometric phase in presence of isotropic decoherence
• Speed limits of the trace distance for open quantum system
• Geometry of the Hilbert space and the Quantum Zeno Effect