Quantum Correlations in Symmetric Multiqubit Systems

Abstract

Permutation symmetric multiqubit quantum states draw attention due to their experimental feasibility and for the mathematical elegance offered by them. This class of states belong to the \(d=2j+1=N+1\) dimensional subspace of the \(2^{N}\) dimensional Hilbert space of N qubits, which corresponds to the maximum value \(j=N/2\) of the angular momentum of N constituent spin-\(\frac{1}{2}\) (qubit) systems. In this article, we review quantum correlations in permutation symmetric multiqubit states via (i) local unitary invariants, pairwise entanglement and spin squeezing (ii) entanglement characterization using covariance matrix (iii) local sum uncertainty relations (LSUR) for symmetric multiqubit systems (iv) Majorana geometric representation of pure symmetric multiqubit states (v) canonical forms of pure symmetric states under stochastic local operations and classical communications (SLOCC).