A universal approach to Krylov state and operator complexities
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2023-09-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.3.080 |
| _version_ | 1797691474036391936 |
|---|---|
| author | Mohsen Alishahiha, Souvik Banerjee |
| author_facet | Mohsen Alishahiha, Souvik Banerjee |
| author_sort | Mohsen Alishahiha, Souvik Banerjee |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T02:13:49Z |
| format | Article |
| id | doaj.art-1459123a5d244fde98924e7d89fac220 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-12T02:13:49Z |
| publishDate | 2023-09-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-1459123a5d244fde98924e7d89fac2202023-09-06T10:20:08ZengSciPostSciPost Physics2542-46532023-09-0115308010.21468/SciPostPhys.15.3.080A universal approach to Krylov state and operator complexitiesMohsen Alishahiha, Souvik BanerjeeWe 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.https://scipost.org/SciPostPhys.15.3.080 |
| spellingShingle | Mohsen Alishahiha, Souvik Banerjee A universal approach to Krylov state and operator complexities SciPost Physics |
| title | A universal approach to Krylov state and operator complexities |
| title_full | A universal approach to Krylov state and operator complexities |
| title_fullStr | A universal approach to Krylov state and operator complexities |
| title_full_unstemmed | A universal approach to Krylov state and operator complexities |
| title_short | A universal approach to Krylov state and operator complexities |
| title_sort | universal approach to krylov state and operator complexities |
| url | https://scipost.org/SciPostPhys.15.3.080 |
| work_keys_str_mv | AT mohsenalishahihasouvikbanerjee auniversalapproachtokrylovstateandoperatorcomplexities AT mohsenalishahihasouvikbanerjee universalapproachtokrylovstateandoperatorcomplexities |