Entanglement robustness of symmetric multiqubit states

Detecting the entanglement of a multipartite pure state is a task that
can now be addressed using various tools, such as for example, negativity
or generalised concurrences. Realising the same task with a mixed
state is however still a challenge today. In a situation where some of
the parties of a multipartite entangled pure state are lost, the question
arises whether the residual mixed state keeps some of the initial
entanglement. In this context, entangled pure states that after partial
trace keep some entanglement are said to be robust against party loss
and those that lose all entanglement (i.e. become separable) are said
to be fragile against party loss. In this talk, we investigate the entanglement
robustness against party loss of symmetric multiqubit states.
We identify all the fragile states for the loss of 1 qubit and show that
these fragile states exhibit a particular symmetry and are all SLOCCequivalent.
We also study robustness properties for multiple parties
loss and treat exhaustively the case of symmetric states of 4 qubits.