SYMMETRIC STATES AND DYNAMICS OF THREE QUANTUM BITS

The unitary group acting on the Hilbert space H:= (C2 )⊗3 of three quantum bits admits a Lie subgroup, US3 (8), of elements which permute with the symmetric group of permutations of three objects. Under the action of such a Lie subgroup, the Hilbert space H splits into three invariant subspaces of dimensions 4, 2 and 2 respectively, each corresponding to an irreducible representation of su(2). The subspace of dimension 4 is uniquely determined and corresponds to states that are themselves invariant under the action of the symmetric group. This is the so called symmetric sector. The subspaces of dimension two are not uniquely determined and we parametrize them all. We provide an analysis of pure states that are in the subspaces invariant under US3 (8). This concerns their entanglement properties, separability criteria and dynamics under the Lie subgroup US3 (8). As a physical motivation for the states and dynamics we study, we propose a physical set-up which consists of a symmetric netw...