Unextendible Maximally Entangled Bases and Mutually Unbiased Bases in ℂ d ⊗ ℂ d′

Constructions of unextendible entangled bases

“…In Section 5, we show that there is a (d(d ′ − 1) + m)-number UMEB in C d ⊗ C d ′ if there exists an unextendible partial Hadamard matrix H m×d . Our constructions generalize and improve most results in [8,9,[11][12][13][14][15][16], and provide new SUEBks and UMEBs.…”

Constructing Mutually Unbiased Bases from Unextendible Maximally Entangled Bases

“…Furthermore, a set of states {|φ i ∈ C d ⊗ C d ′ : i = 1, 2, · · · , n, n < dd ′ } is called an n-member unextendible maximally entangled basis (UMEB) if and only if: (i) |φ i , i = 1, 2, · · · , n are maximally entangled; (ii) φ i |φ j = δ ij ,i, j = 1, 2, · · · , n; (iii) if φ i |ψ = 0, ∀ i = 1, 2, · · · , n, then |ψ cannot be maximally entangled. The constructions of MUBs based on UMEBs in C 2 ⊗ C 3 and C 3 ⊗ C 4 were derived in [11][12][13]. The authors proved that a complete set of mutually unbiased bases of a bipartite system contains a fixed amount of entanglement, independent of the choice of the set [14].…”

Mutually Unbiased Maximally Entangled Bases for the Bipartite System ℂ d ⊗ ℂ d k $\mathbb {C}^{d}\otimes \mathbb {C}^{d^{k}}$

“…In [14] the authors first considered the unextendible maximally entangled bases and mutually unbiased bases. Some systematic ways of constructing mutually unbiased (unextendible) maximally entangled bases in bipartite systems have been presented in [15,16].…”