On the Identication of Symmetric N-qubit Maximally Entangled States

Maximally entangled states can serve as a useful resource in many different contexts. It is therefore important to identify those states. Here we are interested in the identification of maximally entangled states in the symmetric subspace of an N-qubit system. By maximally entangled states, we refer to symmetric states characterized by a one qubit reduced density matrix proportional to the identity. These states maximise various entanglement measures [1] such as von Neumann and Meyer-Wallach entropy and are unique up to LU in their SLOCC class [2]. We identify and characterize all maximally entangled symmetric states up to 4 qubits. We provide general conditions for a symmetric state with an arbitrary number of qubits to be maximally entangled and identify families of SLOCC classes which do not contain any maximally entangled states.

[1] F. Verstraete, J. Dehaene, B. De Moor, Phys. Rev. A 68, 012103 (2003).
[2] G. Gour, N. Wallach, N. J. Phys. 13, 073013 (2011)