Supersinglets and localisable entanglement in permutation Hamiltonian ground states
Sougato Bose
University College London
Abstract: We show that supersinglets naturally arise as the ground state of any connected graph of interacting qudits as long as the graph has d sites and the interaction is a SU(d)-invariant permutation Hamiltonian. This includes a chain coupled only by nearest neighbour interactions. We point out that "local measurements" on some of these qudits, with the freedom of choosing a distinct measurement basis at each qudit randomly from an infinite set of bases, project the remainder onto a singlet state. Two implications of this are (i) that these states have a high persistency of entanglement, and (ii) the possibility of establishing an arbitrary number of ebits of entanglement between separated parties by local measurements, if each party can access more than one qudit of the graph.