We characterize the positive maps detecting the entangled bipartite states of n × n qubits that are diagonal with respect to the orthonormal basis constructed by tensor products of Pauli matrices acting on the totally symmetric state. We then discuss the case n = 2 for a class of states completely determined by the geometric patterns of subsets of a 16 point lattice. PACS numbers:Let M d (C) be the algebra of d × d matrices acting on C d .Definition 2 A linear map Λ : M d1 (C) → M d2 (C) is said to be positive (P) if it sends positive matrices into positive matrices. Let id n : M n (C) ∋ X → X denote the identity map on M n (C). Then, Λ is said to be completely positive (CP) if id n ⊗ Λ is positive on M n (C) ⊗ M d1 (C) for all n ≥ 1.

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