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A universal approach to Krylov State and Operator complexities
by Mohsen Alishahiha, Souvik Banerjee
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Souvik Banerjee |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2212.10583v3 (pdf) |
| Date accepted: | 2023-07-10 |
| Date submitted: | 2023-06-29 19:07 |
| Submitted by: | Banerjee, Souvik |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
List of changes
1. We have added a couple of paragraphs at the end of section IV on the possible connection between holographic subregion complexity and Krylov subregion complexity.
2. We have modified and extended the conclusion section focussing on the practical usefulness and conceptual novelty of our work.
Published as SciPost Phys. 15, 080 (2023)