quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable states. QSL are closely related to time-energy uncertainty relations. In 1945, Leonid Mandelstam and

Igor Tamm Igor Yevgenyevich Tamm ( rus, И́горь Евге́ньевич Тамм , p=ˈiɡərʲ jɪvˈɡʲenʲjɪvitɕ ˈtam , a=Ru-Igor Yevgenyevich Tamm.ogg; 8 July 1895 – 12 April 1971) was a Soviet physicist who received the 1958 Nobel Prize in ...

derived a time-energy uncertainty relation that bounds the speed of evolution in terms of the energy dispersion. Over half a century later,

Norman Margolus Norman H. Margolus (born 1955) is a Canadian-American physicist and computer scientist, known for his work on cellular automata and reversible computing.. He is a research affiliate with the Computer Science and Artificial Intelligence Laborator ...

and Lev Levitin showed that the speed of evolution cannot exceed the mean energy, a result known as the

Margolus–Levitin theorem The Margolus–Levitin theorem states that the processing rate of all forms of computation (including quantum computation) cannot be higher than about 6 × 1033 operations per second per joule of energy. The theorem is named for Norman Margol ...

. Realistic physical systems in contact with an environment are known as

open quantum system In physics, an open quantum system is a quantum-mechanical system that interacts with an external quantum system, which is known as the ''environment'' or a ''bath''. In general, these interactions significantly change the dynamics of the system an ...

s and their evolution is also subject to QSL. Quite remarkably it was shown that environmental effects, such as non-Markovian dynamics can speed up quantum processes, which was verified in a cavity QED experiment. QSL have been used to explore the

limits of computation The limits of computation are governed by a number of different factors. In particular, there are several physical and practical limits to the amount of computation or data storage that can be performed with a given amount of mass, volume, or energ ...

and complexity. In 2017, QSLs were studied in a quantum oscillator at high temperature. In 2018, it was shown that QSL are not restricted to the quantum domain and that similar bounds hold in classical systems. In 2021, both the Mandelstam-Tamm and the Margolus-Levitin QSL bounds were concurrently tested in a single experiment which indicated there are "two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit occurs at longer times."

References

{{reflist Quantum mechanics Mathematical physics