Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.06225 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909679646408704 |
|---|---|
| author | Corey, Daniel Schmidt, Simon Wack, Marcel |
| author_facet | Corey, Daniel Schmidt, Simon Wack, Marcel |
| contents | We define and study a collection of matroid isomorphism games corresponding to various axiomatic characterizations of matroids. These are nonlocal games played between two cooperative players. Each game is played on two matroids, and the matroids are isomorphic if and only if the game has a perfect classical winning strategy. We define notions of quantum isomorphism in terms of perfect quantum commuting strategies, and we find a pair of nonisomorphic matroids that are quantum isomorphic. We also give a purely algebraic characterization of quantum isomorphic matroids. Finally, we use this notion of quantum isomorphism to describe a new type of quantum automorphism group of a matroid and derive a sufficient condition for a matroid to have nonclassical quantum automorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matroid isomorphism games Corey, Daniel Schmidt, Simon Wack, Marcel Quantum Algebra Mathematical Physics Combinatorics 05B35 (Primary), 05E16, 16T30, 20B25 (Secondary) We define and study a collection of matroid isomorphism games corresponding to various axiomatic characterizations of matroids. These are nonlocal games played between two cooperative players. Each game is played on two matroids, and the matroids are isomorphic if and only if the game has a perfect classical winning strategy. We define notions of quantum isomorphism in terms of perfect quantum commuting strategies, and we find a pair of nonisomorphic matroids that are quantum isomorphic. We also give a purely algebraic characterization of quantum isomorphic matroids. Finally, we use this notion of quantum isomorphism to describe a new type of quantum automorphism group of a matroid and derive a sufficient condition for a matroid to have nonclassical quantum automorphism. |
| title | Matroid isomorphism games |
| topic | Quantum Algebra Mathematical Physics Combinatorics 05B35 (Primary), 05E16, 16T30, 20B25 (Secondary) |
| url | https://arxiv.org/abs/2507.06225 |