2010/04/30 by Vlad Gheorghiu, Shiang Yong Looi · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreva.81.062341
published as Phys. Rev. A 81, 062341 (2010) · Minor changes, replaced by the published version. Any comments are welcome!
openalex publication_date 2010/06/25 · arxiv created 2010/06/26 · arxiv updated 2010/06/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Recently, Karimipour and Memarzadeh [Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space, each of dimension D, with the following properties: (i) The family continuously interpolates between a product basis and a maximally entangled basis as some parameter t is varied, and (ii) for a fixed t, all basis states have the same amount of entanglement. The authors derived a necessary condition and provided explicit solutions for D\ensuremath\leqslant5, but the existence of a solution for arbitrary dimensions remained an open problem. We prove that such families exist in arbitrary dimensions by providing two simple solutions, one that employs the properties of quadratic Gauss sums and the other that uses graph states. The latter can be generalized to more than two parties---we can construct equally entangled families that vary continuously between a product basis and a graph-state basis.