A universal approach to Krylov state and operator complexities
Mohsen Alishahiha, Souvik Banerjee
Abstract
We present a general framework in which both Krylov state and operator complexities can be put on the same footing. In our formalism, the Krylov complexity is defined in terms of the density matrix of the associated state which, for the operator complexity, lives on a doubled Hilbert space obtained through the channel-state map. This unified definition of complexity in terms of the density matrices enables us to extend the notion of Krylov complexity, to subregion or mixed state complexities and also naturally to the Krylov mutual complexity. We show that this framework also encompasses nicely the holographic notions of complexity.
Topics & Concepts
Hilbert spaceOperator (biology)MathematicsComputational complexity theoryFormalism (music)State (computer science)Algebra over a fieldComputer scienceAlgorithmTheoretical computer scienceApplied mathematicsPure mathematicsArtRepressorChemistryGeneVisual artsBiochemistryMusicalTranscription factorQuantum many-body systemsAlgebraic structures and combinatorial modelsBlack Holes and Theoretical Physics