Researchers Calculate Fastest Quantum Evolution Using Geodesic Arcs

Sergio Carrasco and Dominique Spehner, at University of Concepción, have derived the explicit form of Bures geodesics, the shortest paths connecting non-faithful density matrices representing quantum states with differing ranks. The derivation extends existing knowledge of quantum speed limits, previously defined for pure and faithful states, and provides a condition for geodesic uniqueness. These findings have implications for understanding the key limits of how sharply quantum systems can change, mirroring the behaviour of great circles on a sphere. Bures geodesic arcs connecting non-faithful density matrices have, for the first time, been explicitly defined, revealing infinitely many shortest paths can exist where previously only one was known. This represents a shift from solely identifying single fastest routes between…