{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:18Z","timestamp":1753893858181,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we introduce a notion of quantum discrepancy, a non-commutative version of combinatorial discrepancy which is defined for projection systems, i.e. finite sets of orthogonal projections, as non-commutative counterparts of set systems. We show that besides its natural algebraic formulation, quantum discrepancy, when restricted to set systems, has a probabilistic interpretation in terms of determinantal processes. Determinantal processes are a family of point processes with a rich algebraic structure.\u00a0 A common feature of this family is the local repulsive behavior of points. Alishahi and Zamani (2015) exploit this repelling property to construct low-discrepancy point configurations on the sphere.\u00a0\r\nWe give an upper bound for quantum discrepancy in terms of $N$, the dimension of the space, and $M$, the size of the projection system, which is tight in a wide range of parameters $N$ and $M$. Then we investigate the relation of these two kinds of discrepancies, i.e. combinatorial and quantum, when restricted to set systems, and bound them in terms of each other.<\/jats:p>","DOI":"10.37236\/7587","type":"journal-article","created":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T04:52:43Z","timestamp":1589518363000},"source":"Crossref","is-referenced-by-count":0,"title":["Quantum Discrepancy: A Non-Commutative Version of Combinatorial Discrepancy"],"prefix":"10.37236","volume":"27","author":[{"given":"Kasra","family":"Alishahi","sequence":"first","affiliation":[]},{"given":"Mohaddeseh","family":"Rajaee","sequence":"additional","affiliation":[]},{"given":"Ali","family":"Rajaei","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,5,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p19\/8076","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p19\/8076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T04:52:43Z","timestamp":1589518363000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/7587","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,5,15]]},"article-number":"P2.19"}}