Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations
Issued Date
2024-12-01
Resource Type
ISSN
24699926
eISSN
24699934
Scopus ID
2-s2.0-85211966947
Journal Title
Physical Review A
Volume
110
Issue
6
Rights Holder(s)
SCOPUS
Bibliographic Citation
Physical Review A Vol.110 No.6 (2024)
Suggested Citation
Wonglakhon N., Wiseman H.M., Chantasri A. Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations. Physical Review A Vol.110 No.6 (2024). doi:10.1103/PhysRevA.110.062207 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/102446
Title
Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations
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Author's Affiliation
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Abstract
Theoretical tools used in processing continuous measurement records from real experiments to obtain quantum trajectories can easily lead to numerical errors due to a noninfinitesimal time resolution. In this work we propose a systematic assessment of the accuracy of a map. We perform error analyses for diffusive quantum trajectories, based on single-Time-step Kraus operators proposed in the literature, and find the orders in time increments Δt, to which such operators satisfy the conditions for valid average quantum evolution (completely positive, convex linear, and trace preserving), and the orders to which they match the Lindblad solutions. Given these error analyses, we propose a Kraus operator that satisfies the valid average quantum evolution conditions and agrees with the Lindblad master equation, to second order in Δt, thus surpassing all other existing approaches. In order to test how well our proposed operator reproduces exact quantum trajectories, we analyze two examples of qubit measurement, where exact maps can be derived: A qubit subjected to a dispersive (z-basis) measurement and a fluorescence (dissipative) measurement. We show analytically that our proposed operator gives the smallest average trace distance to the exact quantum trajectories compared to existing approaches.