Tensor of coherences parameterization of multiqubit density operators for entanglement characterization

Abstract

For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization 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 parameterization, 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 on the possible origin of entanglement for such densities.

15 pages, 3 figures

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• The Volume of Two-Qubit States by Information Geometry
• Elliptical orbits in the Bloch sphere
• Invariance of Bipartite Separability and PPT-Probabilities over Casimir Invariants of Reduced States
• Reflection Symmetries for Multiqubit Density Operators
• Extensions of Generalized Two-Qubit Separability Probability Analyses to Higher Dimensions, Additional Measures and New Methodologies