For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parametrization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parametrization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few-qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight into the possible origin of entanglement for such densities.

• Received 24 July 2003

DOI:https://doi.org/10.1103/PhysRevA.69.012311