{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:14:36Z","timestamp":1753884876485,"version":"3.41.2"},"reference-count":42,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of [Formula: see text] subsystems with [Formula: see text] levels each to the set of complex Hadamard matrices of order [Formula: see text]. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ([Formula: see text] or [Formula: see text]), two-unitary ([Formula: see text] and [Formula: see text] are unitary), or [Formula: see text]-unitary. Here [Formula: see text] denotes reshuffling of a matrix [Formula: see text] describing a bipartite system, and [Formula: see text] its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in [Formula: see text] dimensions. <\/jats:p>","DOI":"10.1142\/s1230161224500082","type":"journal-article","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T05:40:40Z","timestamp":1719898840000},"source":"Crossref","is-referenced-by-count":0,"title":["Multi-Unitary Complex Hadamard Matrices"],"prefix":"10.1142","volume":"31","author":[{"given":"Wojciech","family":"Bruzda","sequence":"first","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, al. Lotnik\u00f3w 32\/46, 02\u2013668 Warszawa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grzegorz","family":"Rajchel-Mieldzio\u0107","sequence":"additional","affiliation":[{"name":"NASK National Research Institute, ul. 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