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Initial-state-dependent quantum speed limit for dissipative state preparation: Framework and optimization

Junjie Liu1,* and Hanlin Nie2,†

  • 1Department of Physics, International Center of Quantum and Molecular Structures, Shanghai University, Shanghai 200444, China
  • 2Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, Singapore 117543

  • *jjliu.fd@gmail.com
  • †e0547610@u.nus.edu
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Phys. Rev. A 107, 052608 – Published 19 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.052608

Abstract

Dissipation has traditionally been considered a hindrance to quantum information processing, but recent studies have shown that it can be harnessed to generate desired quantum states. To be useful for practical applications, the ability to speed up the dissipative evolution is crucial. In this study, we focus on a Markovian dissipative-state-preparation scheme in which the prepared state is one of the energy eigenstates. We derive an initial-state-dependent quantum speed limit (QSL) that offers a more refined measure of the actual evolution time compared to the commonly used initial-state-independent relaxation time. This allows for passive optimization of dissipative evolution across different initial states. By minimizing the dissipated heat during the preparation process, conditioned on the minimization of evolution time using the QSL, we find that the preferred initial state has a specific permutation of diagonal elements with respect to an ordered energy eigenbasis of increasing eigenvalues. In this configuration, the population on the prepared state is the largest, and the remaining diagonal elements are sorted in an order resembling that of a passive state in the same ordered energy eigenbasis. We demonstrate the effectiveness of our strategy in a dissipative Rydberg-atom system for preparing the Bell state. Our work provides insights into the optimization of dissipative-state-preparation processes and could have significant implications for practical quantum technologies.

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Phys. Rev. A 107, 052608– Published 19 May, 2023
  • Received 21 March 2023
  • Accepted 11 May 2023
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