Abstract :
[en] The problem studied by Verstraete, Audenaert and De Moor in [1] -about which global unitary operations maximize the entanglement of a bipartite qubit system- is revisited, extended and solved when permutation symmetry on the qubits is imposed [2]. This condition appears naturally in bosonic systems or spin systems [3]. We fully characterize the set of absolutely separable symmetric states (SAS) for two qubits and provide fairly tight bounds for three qubits. In particular, we find the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimum radius of a ball that includes the set of SAS states, for both two and three qubits.
[1] F. Verstraete, K. Audenaert, and B. De Moor, Phys. Rev. A, 64, 012316, (2001).
[2] J. Martin and E. Serrano-Ensástiga, arXiv:2112.05102.
[3] O. Giraud, P. Braun, and D. Braun, Phys. Rev. A, 78, 042112, (2008).
