Quantum speed limit

In quantum mechanics, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable states.[1] QSL are closely related to time-energy uncertainty relations. In 1945, Leonid Mandelstam and Igor Tamm derived a time-energy uncertainty relation that bounds the speed of evolution in terms of the energy dispersion.[2] Over half a century later, Norman Margolus and Lev Levitin showed that the speed of evolution cannot exceed the mean energy,[3] a result known as the Margolus–Levitin theorem. Realistic physical systems in contact with an environment are known as open quantum systems and their evolution is also subject to QSL.[4][5] Quite remarkably it was shown that environmental effects, such as non-Markovian dynamics can speed up quantum processes,[6] which was verified in a cavity QED experiment.[7]

QSL have been used to explore the limits of computation[8][9] and complexity. In 2017, QSLs were studied in a quantum oscillator at high temperature. [10] In 2018, it was shown that QSL are not restricted to the quantum domain and that similar bounds hold in classical systems. [11][12] In 2021, both the Mandelstam-Tamm and the Margolus-Levitin QSL bounds were concurrently tested in a single experiment[13] 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."