Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in \cd by properties of Guss sums for arbitrary odd d. It improves the known lower bound p^a-1 for odd d. Certainly, it also generalizes the lower bound 2(p^a-1) for d being a single prime power. Furthermore, we construct MUMEBs in \ckd for general k\geq 2 and odd d. We get the similar lower bounds as k,b are both single prime powers. Particularly, when k is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in \ckd, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases.Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in \cd by properties of Guss sums for arbitrary odd d. It improves the known lower bound p^a-1 for odd d. Certainly, it also generalizes the lower bound 2(p^a-1) for d being a single prime power. Furthermore, we construct MUMEBs in \ckd for general k\geq 2 and odd d. We get the similar lower bounds as k,b are both single prime powers. Particularly, when k is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in \ckd, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases.

Quantum Information and ComputationNov 1, 20186 citations

Constructing Mutually Unbiased Bases from Unextendible Maximally Entangled Bases

Hui Zhao, Lin Zhang, Shao-Ming Fei +1 more

arXiv:2001.09515Reports on Mathematical PhysicsFeb 1, 20203 citations

Mutually Unbiased Property of Special Entangled Bases

Yuan-Hong Tao, Xin-Lei Yong, Yi-Fan Han +2 more

International Journal of Theoretical PhysicsJun 29, 20210 citations

New bounds of Mutually unbiased maximally entangled bases in C^d\otimes C^{kd}

Xiaoya Cheng, Yun Shang

Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in C^d\otimes C^d by properties of Guss sums for arbitrary odd d. It improves the known lower bound p^a-1 for odd d. Certainly, it also generalizes the lower bound 2(p^a-1) for d being a single prime power. Furthermore, we construct MUMEBs in C^d\otimes C^{kd} for general k>= 2 and odd d. We get the similar lower bounds as $k,b$ are both single prime powers. Particularly, when k is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in C^d\otimes C^{kd}, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases.Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in C^d\otimes C^d by properties of Guss sums for arbitrary odd d. It improves the known lower bound p^a-1 for odd d. Certainly, it also generalizes the lower bound 2(p^a-1) for d being a single prime power. Furthermore, we construct MUMEBs in C^d\otimes C^{kd} for general k>= 2 and odd d. We get the similar lower bounds as $k,b$ are both single prime powers. Particularly, when k is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in C^d\otimes C^{kd}, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases.

arXiv:1710.07458Oct 20, 20172 citations

Unextendible Maximally Entangled Bases and Mutually Unbiased Bases in Multipartite Systems

Yajing Zhang, Hui Zhao, Naihuan Jing +1 more

arXiv:1708.04171International Journal of Theoretical PhysicsAug 11, 20178 citations

Mutually unbiased maximally entangled bases from difference matrices

Yajuan Zang, Zihong Tian, Hui-Juan Zuo +1 more

Abstract Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish q mutually unbiased bases with q − 1 maximally entangled bases and one product basis in C q ⊗ C q for arbitrary prime power q . In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in C 12 ⊗ C 12 and C 21 ⊗ C 21 , which improve the known lower bounds for d = 3 m , with (3, m ) = 1 in C d ⊗ C d . Furthermore, we construct p + 1 mutually unbiased bases with p maximally entangled bases and one product basis in C p ⊗ C p 2 for arbitrary prime number p .Abstract Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish q mutually unbiased bases with q − 1 maximally entangled bases and one product basis in C q ⊗ C q for arbitrary prime power q . In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in C 12 ⊗ C 12 and C 21 ⊗ C 21 , which improve the known lower bounds for d = 3 m , with (3, m ) = 1 in C d ⊗ C d . Furthermore, we construct p + 1 mutually unbiased bases with p maximally entangled bases and one product basis in C p ⊗ C p 2 for arbitrary prime number p .

arXiv:2210.01517Journal of Physics A Mathematical and TheoreticalSep 14, 20225 citations

k,b

are both single prime powers. Particularly, when k is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in C^d\otimes C^{kd}, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases.