Entanglement witnesses for a class of bipartite states of n x n qubits

TL;DR

This paper develops entanglement witnesses tailored for a specific class of bipartite n x n qubit states, using positive maps and geometric patterns, advancing the detection of entanglement in symmetric states.

Contribution

It introduces a characterization of positive maps for detecting entanglement in diagonal bipartite qubit states, focusing on symmetric states and geometric subset patterns.

Findings

Characterized positive maps for entanglement detection in diagonal bipartite states.

Analyzed the n=2 case with geometric subset patterns on a 16-point lattice.

Provided a framework for identifying entanglement in symmetric qubit states.

Abstract

We characterize the positive maps detecting the entangled bipartite states of n x 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.