{"paper":{"title":"Extremal Marginal States of Maximal Rank in $(d, d+m)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Indu Bala, Swapan Rana","submitted_at":"2026-05-26T12:18:51Z","abstract_excerpt":"We study the extreme points of the convex set $\\mathcal{C}(\\rho_1,\\rho_2)$ of bipartite quantum states with fixed marginals $\\rho_1$ and $\\rho_2$. We construct extreme points in $(d,\\,d+m)$ dimension, of rank $d+m$, matching the highest possible value, for all $d\\geq 3$, $m > \\frac{d^2-2d-2}{2}$ (when $d=2$, $m\\geq 1$). This proves the existence of extremal states with relatively large rank and also covers all the known examples. We further show that, in order to analyze the extreme points of $\\mathcal{C}(\\rho_1,\\rho_2)$, it is sufficient to study the special case $\\mathcal{C}(\\mathcal{D}_1,\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26920","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26920/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}