Rényi mutual information in quantum field theory, tensor networks, and gravity
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929473363902464 |
|---|---|
| author | Kudler-Flam, Jonah Nie, Laimei Vijay, Akash |
| author_facet | Kudler-Flam, Jonah Nie, Laimei Vijay, Akash |
| contents | We explore a large class of correlation measures called the $α-z$ Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the $α-z$ RMIs are positive semi-definite and monotonically decreasing under quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of $α$ and $z$, the $α-z$ RMIs also lower bound connected correlation functions. We develop an easily implementable replica trick which enables us to compute the $α-z$ RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rényi mutual information in quantum field theory, tensor networks, and gravity Kudler-Flam, Jonah Nie, Laimei Vijay, Akash High Energy Physics - Theory Statistical Mechanics Quantum Physics We explore a large class of correlation measures called the $α-z$ Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the $α-z$ RMIs are positive semi-definite and monotonically decreasing under quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of $α$ and $z$, the $α-z$ RMIs also lower bound connected correlation functions. We develop an easily implementable replica trick which enables us to compute the $α-z$ RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography. |
| title | Rényi mutual information in quantum field theory, tensor networks, and gravity |
| topic | High Energy Physics - Theory Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2308.08600 |