Time-optimal quantum transformations with bounded bandwidth

Dan Allan, Niklas Hörnedal, and Ole Andersson

Fysikum, Stockholms universitet, 106 91 Stockholm, Sweden

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In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is initially in an incoherent state relative to the observable and that the state evolves according to a von Neumann equation with a Hamiltonian whose bandwidth is uniformly bounded. The transformation time depends intricately on the observable's and the initial state's eigenvalue spectrum and the relative constellation of the associated eigenspaces. The problem of finding quantum speed limits consequently divides into different cases requiring different strategies. We derive quantum speed limits in a large number of cases, and we simultaneously develop a method to break down complex cases into manageable ones. The derivations involve both combinatorial and differential geometric techniques. We also study multipartite systems and show that allowing correlations between the parts can speed up the transformation time. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.

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Cited by

[1] Niklas Hörnedal and Ole Sönnerborn, "Tight lower bounds on the time it takes to generate a geometric phase", Physica Scripta 98 10, 105108 (2023).

[2] Akram Touil, Barış Çakmak, and Sebastian Deffner, "Ergotropy from quantum and classical correlations", Journal of Physics A: Mathematical and Theoretical 55 2, 025301 (2022).

[3] Sebastian Deffner, "Quantum speed-limited depletion of physical resources", Quantum Views 5, 55 (2021).

[4] Maxwell Aifer and Sebastian Deffner, "From quantum speed limits to energy-efficient quantum gates", New Journal of Physics 24 5, 055002 (2022).

[5] Nikolai Il'in and Oleg Lychkovskiy, "Quantum speed limit for thermal states", Physical Review A 103 6, 062204 (2021).

[6] Nikolai Il`in and Oleg Lychkovskiy, "Quantum speed limit for thermal states", arXiv:2005.06416, (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 21:19:06) and SAO/NASA ADS (last updated successfully 2024-05-24 21:19:08). The list may be incomplete as not all publishers provide suitable and complete citation data.

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