2023/05/30 by Wojciech Bruzda, Bruzda, Wojciech, Grzegorz Rajchel-Mieldzioć +3
Computer Science · #05B20 #46N50 #51F25 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2306.00999
openalex publication_date 2023/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 2k subsystems with d levels each to the set of complex Hadamard matrices of order N=dk. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual (H=H\rm R or H=H\rmΓ), two-unitary (HR and HΓ are unitary), or k-unitary. Here X\rm R denotes reshuffling of a matrix X describing a bipartite system, and X\rm Γ 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 1+1 dimensions.