Abstract :
[en] The problem studied by Verstraete, Audenaert and De Moor [1] -about the global unitary operations that maximise the entanglement of a bipartite system of qubits- is revisited and solved when we consider the permutation symmetry between the qubits [2]. This condition appears naturally in bosonic or spin-1 systems [3]. Our results also allow us to characterise the set of symmetric absolutely separable states (SAS). For symmetric 3-qubit systems, we present numerical calculations for the maximum entanglement and analytical wirnesses for absolute separability. As an application of our results, we analyse the temperature dependence of the maximum entanglement that can be obtained from the thermal state of a spin-1 system with a spin-squeezing Hamiltonian. [1] F. Verstraete, K. Audenaert, and B. De Moor, Phys. Rev. A, 64, 012316, (2001).
[2] E. Serrano-Ensástiga, and J. Martin, SciPost Phys. 15, 120 (2023).
[3] O. Giraud, P. Braun, and D. Braun, Phys. Rev. A, 78, 042112, (2008).
