| Title: |
Local Transformations of Bipartite Entanglement Are Rigid |
| Authors: |
Bostanci, John; Metger, Tony; Yuen, Henry |
| Contributors: |
John Bostanci and Tony Metger and Henry Yuen |
| Publisher Information: |
Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Publication Year: |
2026 |
| Collection: |
DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Subject Terms: |
Uhlmann’s theorem; quantum entanglement; stability theorems |
| Description: |
Uhlmann’s theorem is a fundamental result in quantum information theory that quantifies the optimal overlap between two bipartite pure states after applying local unitary operations (called Uhlmann transformations). We show that optimal Uhlmann transformations are rigid - in other words, they must be unique up to some well-characterized degrees of freedom. This rigidity is also robust: Uhlmann transformations achieving near-optimal overlaps must be close to the unique optimal transformation (again, up to well-characterized degrees of freedom). We describe two applications of our robust rigidity theorem: (a) we obtain better interactive proofs for synthesizing Uhlmann transformations and (b) we obtain a simple, alternative proof of the Gowers-Hatami theorem on the stability of approximate representations of finite groups. |
| Document Type: |
article in journal/newspaper; conference object |
| File Description: |
application/pdf |
| Language: |
English |
| Relation: |
Is Part Of LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.26 |
| DOI: |
10.4230/LIPIcs.ITCS.2026.26 |
| Availability: |
https://doi.org/10.4230/LIPIcs.ITCS.2026.26; https://nbn-resolving.org/urn:nbn:de:0030-drops-253138; https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.26 |
| Rights: |
https://creativecommons.org/licenses/by/4.0/legalcode |
| Accession Number: |
edsbas.AC2898EC |
| Database: |
BASE |