| _version_ | 1866901688314494976 |
|---|---|
| author | Leighton-Trudel, Beau |
| author_facet | Leighton-Trudel, Beau |
| contents | <p>We announce the Mutual–Information Jewel distance</p> <p> d_E(A,B) = K₀ / √I(A:B) ,</p> <p>where I(A:B) is the quantum mutual information between two regions of a many-body state.</p> <p>Jewel Theorem. If I(r) ∝ r^(–X) with 0 < X ≤ 2 (the scaling realised in 1-D conformal critical points), then 1/I is a kernel of negative type and d_E is a bona-fide metric that embeds isometrically in a Hilbert space. The special case X = 2 yields d_E(r) ∝ r, reproducing a Euclidean ruler from entanglement data alone.</p> <p>Full proofs, XXZ benchmarks, and dynamical light-cone validation will appear in a forthcoming submission.</p> <p>SHA-256 digest of the complete draft (v0.9):<br>01c35bce761471261d09ddf522f9467fc1d28dbc556ce13e9587f1ed039f25b9</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15549470 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Priority Notice: The Mutual-Information Jewel Metric Leighton-Trudel, Beau quantum information; distance metric; mutual information <p>We announce the Mutual–Information Jewel distance</p> <p> d_E(A,B) = K₀ / √I(A:B) ,</p> <p>where I(A:B) is the quantum mutual information between two regions of a many-body state.</p> <p>Jewel Theorem. If I(r) ∝ r^(–X) with 0 < X ≤ 2 (the scaling realised in 1-D conformal critical points), then 1/I is a kernel of negative type and d_E is a bona-fide metric that embeds isometrically in a Hilbert space. The special case X = 2 yields d_E(r) ∝ r, reproducing a Euclidean ruler from entanglement data alone.</p> <p>Full proofs, XXZ benchmarks, and dynamical light-cone validation will appear in a forthcoming submission.</p> <p>SHA-256 digest of the complete draft (v0.9):<br>01c35bce761471261d09ddf522f9467fc1d28dbc556ce13e9587f1ed039f25b9</p> |
| title | Priority Notice: The Mutual-Information Jewel Metric |
| topic | quantum information; distance metric; mutual information |
| url | https://doi.org/10.5281/zenodo.15549470 |