Speaker: Takato Mori (Rikkyo University)

Date and time : March 31th,  16:00-

Style: Zoom

Title: Krylov complexity of purification

Abstract: How does a state explore a vast Hilbert as it evolves in time? We answer to this question by considering Krylov complexity, which I will review in the talk. While its notion has been proposed in earlier literature, there has been two formulations: operator complexity and spread/state complexity. The former targets an operator living in an operator space and the latter deals with a pure state living in a Hilbert space. These two formulations are distinct and their relationship has remained unclear. In this work, we introduce Krylov complexity of purification, bridging these two ideas by purification. This quantity can quantify how far a mixed state explores in the state space in a unified manner. We also discuss its nature from various angles including non-unitary evolution, Lloyd-like thermodynamic bound, and mutual complexity. This talk is based on Phys. Rev. Lett. 136, 030201 with Rathindra Nath Das.