Holographic Interpretation of Relative State Complexity
We investigate a large-<i>N</i> conformal field theory (CFT) in a high-energy pure state coupled to a small auxiliary system of <i>M</i> weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an effect...
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| Format: | Article |
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MDPI AG
2020-07-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/6/8/100 |
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| author | Alexander Yosifov Aditya Iyer Lachezar Filipov |
| author_facet | Alexander Yosifov Aditya Iyer Lachezar Filipov |
| author_sort | Alexander Yosifov |
| collection | DOAJ |
| description | We investigate a large-<i>N</i> conformal field theory (CFT) in a high-energy pure state coupled to a small auxiliary system of <i>M</i> weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an effective low-energy notion of computational cost in the bulk, i.e., to the minimal depth of the quantum circuit required to decode its gravitational dual. In light of this, using Nielsen’s approach, a new measure of quantum chaos in terms of the evolution of circuit complexity is proposed. It suggests that studying the evolution of circuit complexity of the auxiliary system can teach us about the chaotic properties of the large-<i>N</i> CFT. This new diagnostic for quantum chaos has important implications for the interior dynamics of evaporating black holes as it implies the radiated Hawking cloud is pseudorandom. |
| first_indexed | 2024-03-10T18:19:16Z |
| format | Article |
| id | doaj.art-cd48f7ddb07741f58ded9d9761ea76fe |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T18:19:16Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-cd48f7ddb07741f58ded9d9761ea76fe2023-11-20T07:30:45ZengMDPI AGUniverse2218-19972020-07-016810010.3390/universe6080100Holographic Interpretation of Relative State ComplexityAlexander Yosifov0Aditya Iyer1Lachezar Filipov2Space Research and Technology Institute, Bulgarian Academy of Sciences, Akad. G. Bonchev Street, Building 1, 1113 Sofia, BulgariaDepartment of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UKSpace Research and Technology Institute, Bulgarian Academy of Sciences, Akad. G. Bonchev Street, Building 1, 1113 Sofia, BulgariaWe investigate a large-<i>N</i> conformal field theory (CFT) in a high-energy pure state coupled to a small auxiliary system of <i>M</i> weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an effective low-energy notion of computational cost in the bulk, i.e., to the minimal depth of the quantum circuit required to decode its gravitational dual. In light of this, using Nielsen’s approach, a new measure of quantum chaos in terms of the evolution of circuit complexity is proposed. It suggests that studying the evolution of circuit complexity of the auxiliary system can teach us about the chaotic properties of the large-<i>N</i> CFT. This new diagnostic for quantum chaos has important implications for the interior dynamics of evaporating black holes as it implies the radiated Hawking cloud is pseudorandom.https://www.mdpi.com/2218-1997/6/8/100black holesquantum informationquantum complexityquantum chaos |
| spellingShingle | Alexander Yosifov Aditya Iyer Lachezar Filipov Holographic Interpretation of Relative State Complexity Universe black holes quantum information quantum complexity quantum chaos |
| title | Holographic Interpretation of Relative State Complexity |
| title_full | Holographic Interpretation of Relative State Complexity |
| title_fullStr | Holographic Interpretation of Relative State Complexity |
| title_full_unstemmed | Holographic Interpretation of Relative State Complexity |
| title_short | Holographic Interpretation of Relative State Complexity |
| title_sort | holographic interpretation of relative state complexity |
| topic | black holes quantum information quantum complexity quantum chaos |
| url | https://www.mdpi.com/2218-1997/6/8/100 |
| work_keys_str_mv | AT alexanderyosifov holographicinterpretationofrelativestatecomplexity AT adityaiyer holographicinterpretationofrelativestatecomplexity AT lachezarfilipov holographicinterpretationofrelativestatecomplexity |