In order to determine how fast quantum technologies can ultimately operate, physicists have established the concept of "quantum speed limits." Quantum speed limits impose limitations on how fast a quantum system can transition from one state to another, so that such a transition requires a minimum amount of time (typically on the order of nanoseconds). This means, for example, that a future quantum computer will not be able to perform computations faster than a certain time determined by these limits.
Ref: Generalized Geometric Quantum Speed Limits. Physical Review X (2 June 2016) | DOI: 10.1103/PhysRevX.6.021031
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. We 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, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our 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. We illustrate our 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. Our 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.