Techniques from information geometry have been used to show that there are an infinite number of quantum speed limits. They also develop a way to determine which of these speed limits are the strictest, or in other words, which speed limits offer the tightest lower bounds. As the researchers explain, the search for the ultimate quantum speed limits is closely related to the very nature of time itself.

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. They investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, they establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Their work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information.

Researchers illustrated their findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Their results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

*Illustration of geometric quantum speed limits. The ultimate speed limit arises from the length of the shortest geodesic path between two states, which here is the dashed blue curve.*

In the future, the researchers plan to experimentally investigate the quantum speed limits derived here using nuclear magnetic resonance (NMR) techniques.

Arxiv- Generalized Geometric Quantum Speed Limits (7 pages)

SOURCES- Physical Review X, Arxiv, Phys Org

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