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Exact quantum speed limits

Arun K. Pati1, Brij Mohan2,3,*, Sahil4,5, and Samuel L. Braunstein6

  • *Contact author: brijhcu@gmail.com
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Phys. Rev. A 112, 062209 – Published 5 December, 2025

DOI: https://doi.org/10.1103/mmzc-fyr9

Abstract

The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this we derive exact quantum speed limits for the unitary dynamics of pure-state quantum systems that outperform the existing quantum speed limits. Using these exact quantum speed limits, we can precisely estimate the evolution time for two- and higher-dimensional quantum systems. Additionally, for both finite- and infinite-dimensional quantum systems, we derive an improved Mandelstam-Tamm bound for pure states and show that this bound always saturates for any unitary generated by self-inverse Hamiltonians. Furthermore, we show that our speed limits establish an upper bound on the quantum computational circuit complexity and yield a tighter quantum Cramér-Rao bound. These results will have a significant impact on our understanding of quantum physics as well as rapidly developing quantum technologies, such as quantum computing, quantum control, and quantum batteries.

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Phys. Rev. A 112, 062209– Published 5 December, 2025
  • Received 12 August 2025
  • Accepted 16 October 2025
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