paper

Krylov complexity of purification

arXiv:2408.00826 · doi:10.1103/qgcx-wxpd

Abstract

In quantum systems, purification can map mixed states into pure states and a non-unitary evolution into a unitary one by enlarging the Hilbert space. We establish a connection between the complexities of mixed quantum states and their purification, proposing new inequalities among these complexities. By examining single qubits, two-qubit Werner states, eight-dimensional Gaussian random unitary ensembles, and infinite-dimensional systems, we demonstrate how these relationships manifest across a broad class of systems. We find that the spread complexity of purification of a vacuum state evolving into a thermal state equals the average number of Rindler particles. This complexity is also shown to adhere to the Lloyd-like bound, indicating a further relation to the quantum speed limit. Finally, using mutual Krylov complexity, we observe subadditivity of the Krylov complexities, which contrasts with known results from holographic volume complexity. We put forward Krylov mutual complexity as a diagnosis of a potential gravity dual of Krylov complexities.

11 pages, 5 figures; Lloyd bound with the energy is added and a slight rearrangement of texts, typos are corrected, references are added (v2); numerical results of random matrix ensemble are added and the whole text is reorganized (v3); published version in PRL (v4)

References in corpus (43)