Quantum Correlations and Permutation Symmetries

In this paper, the connections between quantum non-locality and permutation symmetries areexplored. This includes two types of symmetries: permutation across a superposition and permutationof qubits in a quantum system. An algorithm is proposed for nding the separability class ofa quantum state using a method based on factorizing an arbitrary multipartite state into possiblepartitions, cyclically permuting qubits of the vectors in a superposition to check which separabilityclass it falls into and thereafter using a reduced density-matrix analysis of the system is proposed.For the case of mixed quantum states, conditions for separability are found in terms of the partialtransposition of the density matrices of the quantum system. One of these conditions turns out tobe the Partial Positive Transpose (PPT) condition. A graphical method for analyzing separabilityis also proposed. The concept of permutation of qubits is shown to be useful in dening a newentanglement measure in the `engle'.