N qubits can be entangled in two different ways

HU Yu-a

A scheme for controlled two-way quantum teleportation of unknown one-qubit state via GHZ quadripartite entangled state was proposed.Two sides of communication(Alice and Bob)and the controller,secretly share two pairs of GHZ quadripartite entangled state in advance to construct quantum channel.According to the different ways of distribution along with different measuring vectors choosed to use,two-way quantum teleportation controlled by a third party and a fouth party were realized.After communication,Alice and Bob perform quantum projection measurement on parts of their qubits respectively.If the controller agrees to intercommunication,he should measure his qubits and announce the results via classical channel.Then the both sides of communication can make appropriate unitary transformations on their own certain qubit on the basis of the controller′s results,thus they are able to reconstruct each other′s unknown state on their own qubit.The security of the whole two-way communication is greatly impoved owing to the join of the third party Charlie and the fourth party Dennis.

Richard J. Fitzgerald

Renán Cabrera, W. E. Baylis

Frank Verstraete, Jeroen Dehaene, Bart De Moor +1 more

We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.

Dafa Li

Gabriele Cobucci, Armin Tavakoli

Complex forms of quantum entanglement can arise in two qualitatively different ways: either between many qubits or between two particles with higher-than-qubit dimension. While both the many-qubit frontier and the high-dimension frontier are well established, state-of-the-art quantum technology is becoming increasingly able to create and manipulate entangled states that simultaneously feature many particles and high dimension. Here, we investigate generic states that can be considered both genuinely high-dimensional and genuine multiparticle entangled. We consider a natural quantity that characterizes this key property. To detect it, we develop three different classes of criteria. These enable us both to probe the ultimate noise tolerance of this form of entanglement and to make detection schemes using sparse or even minimal measurement resources. The approach provides a simple way of benchmarking entanglement dimensionality in the multiparticle regime and general, platform-independent, detection methods that readily apply to experimental use.