Closed systems refuting quantum-speed-limit hypotheses

Abstract

Many quantum speed limits for isolated systems can be generalized to also apply to closed systems. This is, for example, the case with the well-known Mandelstam-Tamm quantum speed limit. Margolus and Levitin derived an equally well-known and ostensibly related quantum speed limit, and it seems to be widely believed that the Margolus-Levitin quantum speed limit can be similarly generalized to closed systems. However, a recent geometrical examination of this limit reveals that it differs significantly from most known quantum speed limits. In this paper, we show that, contrary to the common belief, the Margolus-Levitin quantum speed limit does not extend to closed systems in an obvious way. More precisely, we show that for every hypothetical bound of Margolus-Levitin type, there are closed systems that evolve with a conserved normalized expected energy between states with any given fidelity in a time shorter than the bound. We also show that for isolated systems, the Mandelstam-Tamm quantum speed limit and a slightly weakened version of this limit that we call the Bhatia-Davies quantum speed limit always saturate simultaneously. Both of these evolution time estimates extend straightforwardly to closed systems. We demonstrate that there are closed systems that saturate the Mandelstam-Tamm but not the Bhatia-Davies quantum speed limit.

arXiv comment5 pages, 3 figures, identical to the published article

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Cited by in corpus (7)

• Margolus-Levitin quantum speed limit for an arbitrary fidelity
• Quantum Speed Limits Based on Schatten Norms: Universality and Tightness
• Tight lower bounds on the time it takes to generate a geometric phase
• Family of attainable geometric quantum speed limits
• Isoholonomic inequality and tight implementations of holonomic quantum gates
• Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
• Systems that saturate the Margolus-Levitin quantum speed limit