A universal approach to Krylov state and operator complexities

Alishahiha, Mohsen; Banerjee, Souvik

doi:10.21468/SciPostPhys.15.3.080

SciPost Physics

A universal approach to Krylov state and operator complexities

Mohsen Alishahiha, Souvik Banerjee

SciPost Phys. 15, 080 (2023) · published 6 September 2023

doi: 10.21468/SciPostPhys.15.3.080
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.3.080
TI  - A universal approach to Krylov state and operator complexities
PY  - 2023/09/06
UR  - https://scipost.org/SciPostPhys.15.3.080
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 3
SP  - 080
A1  - Alishahiha, Mohsen
AU  - Banerjee, Souvik
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.3.080,
	title={{A universal approach to Krylov state and operator complexities}},
	author={Mohsen Alishahiha and Souvik Banerjee},
	journal={SciPost Phys.},
	volume={15},
	pages={080},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.3.080},
	url={https://scipost.org/10.21468/SciPostPhys.15.3.080},
}

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Iizuka et al., Krylov complexity in the IP matrix model. Part II
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Gautam et al., Spread complexity evolution in quenched interacting quantum systems
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Complexity theory

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¹ Mohsen Alishahiha,
² ³ Souvik Banerjee