Entanglement of the Antisymmetric State

Matthias Christandl, Norbert Schuch, Andreas Winter

Fumitaka Yura

We show that the entanglement cost of the three-dimensional antisymmetric states is one ebit.

Paul Cummins

Masahito Hayashi, Damian Markham, Mio Murao +2 more

We study various distancelike entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement, and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be permutation symmetric. This allows us to calculate the explicit values of various entanglement measures for symmetric and antisymmetric basis states, observing that antisymmetric states are generally more entangled. We use these results to obtain a variety of interesting ensembles of quantum states for which the optimal local operations and classical communication discrimination probability may be explicitly determined and achieved. We also discuss applications to the construction of optimal entanglement witnesses.

Ludovic Arnaud

We investigate the intermediate permutational symmetries of a system of qubits that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits picked at random with respect to the uniform measure on the unit sphere of the Hilbert space are almost as antisymmetric as they are allowed to be. We then observe that multipartite entanglement, measured by the generalized Meyer-Wallach measure, tends to be larger in subspaces that are more antisymmetric than the complete symmetric one. Eventually, we prove that all states contained in the most antisymmetric subspace are relevant multipartite entangled states in the sense that their 1-qubit reduced states are all maximally mixed.