Alternating minimization for computing doubly minimized Petz Renyi mutual information
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912469336719360 |
|---|---|
| author | Burri, Laura |
| author_facet | Burri, Laura |
| contents | The doubly minimized Petz Renyi mutual information (PRMI) of order $α$ is defined as the minimization of the Petz divergence of order $α$ of a fixed bipartite quantum state $ρ_{AB}$ relative to any product state $σ_A\otimes τ_B$. To date, no closed-form expression for this measure has been found, necessitating the development of numerical methods for its computation. In this work, we show that alternating minimization over $σ_A$ and $τ_B$ asymptotically converges to the doubly minimized PRMI for any $α\in (\frac{1}{2},1)\cup (1,2]$, by proving linear convergence of the objective function values with respect to the number of iterations for $α\in (1,2]$ and sublinear convergence for $α\in (\frac{1}{2},1)$. Previous studies have only addressed the specific case where $ρ_{AB}$ is a classical-classical state, while our results hold for any quantum state $ρ_{AB}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Alternating minimization for computing doubly minimized Petz Renyi mutual information Burri, Laura Quantum Physics Information Theory The doubly minimized Petz Renyi mutual information (PRMI) of order $α$ is defined as the minimization of the Petz divergence of order $α$ of a fixed bipartite quantum state $ρ_{AB}$ relative to any product state $σ_A\otimes τ_B$. To date, no closed-form expression for this measure has been found, necessitating the development of numerical methods for its computation. In this work, we show that alternating minimization over $σ_A$ and $τ_B$ asymptotically converges to the doubly minimized PRMI for any $α\in (\frac{1}{2},1)\cup (1,2]$, by proving linear convergence of the objective function values with respect to the number of iterations for $α\in (1,2]$ and sublinear convergence for $α\in (\frac{1}{2},1)$. Previous studies have only addressed the specific case where $ρ_{AB}$ is a classical-classical state, while our results hold for any quantum state $ρ_{AB}$. |
| title | Alternating minimization for computing doubly minimized Petz Renyi mutual information |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2507.05205 |