Midpoint BKM Estimates and Boundary Coherence
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913113439207424 |
|---|---|
| author | Nasreddine, Hassan |
| author_facet | Nasreddine, Hassan |
| contents | We study lower bounds for the quantum relative entropy between a density matrix and its block-diagonal part. For a block matrix with diagonal blocks A,C>0 and off-diagonal coherence block B, we prove a lower bound expressed through the associated Bogoliubov--Kubo--Mori (BKM) kernel.
The proof uses a midpoint estimate for the BKM Hessian along the affine interpolation between the matrix and its block-diagonal projection. The resulting estimate is genuinely noncommutative and retains information about the joint spectral structure of the diagonal blocks and the coherence term.
As a consequence, under a spectral gap condition on A relative to C, we obtain an explicit logarithmic lower bound proportional to the squared Frobenius norm of the coherence block. The appearance of the BKM metric is natural in this setting because it coincides with the Hessian of quantum relative entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Midpoint BKM Estimates and Boundary Coherence Nasreddine, Hassan Quantum Physics Mathematical Physics Primary 81P45, Secondary 47A63, 94A17 We study lower bounds for the quantum relative entropy between a density matrix and its block-diagonal part. For a block matrix with diagonal blocks A,C>0 and off-diagonal coherence block B, we prove a lower bound expressed through the associated Bogoliubov--Kubo--Mori (BKM) kernel. The proof uses a midpoint estimate for the BKM Hessian along the affine interpolation between the matrix and its block-diagonal projection. The resulting estimate is genuinely noncommutative and retains information about the joint spectral structure of the diagonal blocks and the coherence term. As a consequence, under a spectral gap condition on A relative to C, we obtain an explicit logarithmic lower bound proportional to the squared Frobenius norm of the coherence block. The appearance of the BKM metric is natural in this setting because it coincides with the Hessian of quantum relative entropy. |
| title | Midpoint BKM Estimates and Boundary Coherence |
| topic | Quantum Physics Mathematical Physics Primary 81P45, Secondary 47A63, 94A17 |
| url | https://arxiv.org/abs/2605.11024 |