Effect of measurements on quantum speed limit

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 measur...

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Bibliographic Details
Published in:Europhysics letters 2024-06, Vol.146 (6), p.60001
Main Authors: Srivastav, Abhay, Pandey, Vivek, Pati, Arun K.
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Hamiltonian functions
Hilbert space
Quantum computing
Quantum theory
Speed limits
State vectors
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/ad56c2