Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states

The first characterization of mixed-state entanglement was achieved for two-qubit states in Werner's seminal work [Phys. Rev. A 40, 4277 (1989)]. A physically important extension of this result concerns mixtures of a pure entangled state (such as the Greenberger-Horne-Zeilinger [GHZ] state) and the completely unpolarized state. These mixed states serve as benchmark for the robustness of entanglement. They share the same symmetries as the GHZ state. We call such states GHZ-symmetric. Despite significant progress their multipartite entanglement properties have remained an open problem. Here we give a complete description of the entanglement in the family of three-qubit GHZ-symmetric states and, in particular, of the three-qubit generalized Werner states. Our method relies on the appropriate parameterization of the states and on the invariance of entanglement properties under general local operations. An immediate application of our results is the definition of a symmetrization witness for the entanglement class of arbitrary three-qubit states.Comment: 4 pages, 2 figure

Implementation of the Deutsch-Jozsa algorithm with Josephson charge qubits

We investigate the realization of a simple solid-state quantum computer by implementing the Deutsch-Jozsa algorithm in a system of Josephson charge qubits. Starting from a procedure to carry out the one-qubit Deutsch-Jozsa algorithm we show how the N-qubit version of the Bernstein-Vazirani algorithm can be realized. For the implementation of the three-qubit Deutsch-Jozsa algorithm we study in detail a setup which allows to produce entangled states.Comment: accepted for publication in Journal of Modern Optic

Partial transpose as a direct link between concurrence and negativity

Detection of entanglement in bipartite states is a fundamental task in quantum information. The first method to verify entanglement in mixed states was the partial-transpose criterion. Subsequently, numerous quantifiers for bipartite entanglement were introduced, among them concurrence and negativity. Surprisingly, these quantities are often treated as distinct or independent of each other. The aim of this contribution is to highlight the close relations between these concepts, to show the connections between seemingly independent results, and to present various estimates for the mixed-state concurrence within the same framework.Comment: 10 pages, 3 figure

Advanced control with a Cooper-pair box: stimulated Raman adiabatic passage and Fock-state generation in a nanomechanical resonator

The rapid experimental progress in the field of superconducting nanocircuits gives rise to an increasing quest for advanced quantum-control techniques for these macroscopically coherent systems. Here we demonstrate theoretically that stimulated Raman adiabatic passage (STIRAP) should be possible with the quantronium setup of a Cooper-pair box. The scheme appears to be robust against decoherence and should be realizable even with the existing technology. As an application we present a method to generate single-phonon states of a nanomechnical resonator by vacuum-stimulated adiabatic passage with the superconducting nanocircuit coupled to the resonator

Maximum N-body correlations do not in general imply genuine multipartite entanglement

The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong N-party correlations with N-party entanglement in an N-partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest N-party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest N-party correlations may be a tensor product of Bell states, that is, partially separable. We show this by introducing several novel tools for handling the Bloch representation

Tangles of superpositions and the convex-roof extension

We discuss aspects of the convex-roof extension of multipartite entanglement measures, that is, SL(2,\CC) invariant tangles. We highlight two key concepts that contain valuable information about the tangle of a density matrix: the {\em zero-polytope} is a convex set of density matrices with vanishing tangle whereas the {\em convex characteristic curve} readily provides a non-trivial lower bound for the convex roof and serves as a tool for constructing the convex roof outside the zero-polytope. Both concepts are derived from the tangle for superpositions of the eigenstates of the density matrix. We illustrate their application by considering examples of density matrices for two-qubit and three-qubit states of rank 2, thereby pointing out both the power and the limitations of the concepts.Comment: 7 pages, 5 figures, revtex