Detecting multipartite entanglement

@article{Doherty2005DetectingME,
  title={Detecting multipartite entanglement},
  author={Andrew C. Doherty and Pablo A. Parrilo and Federico M. Spedalieri},
  journal={Physical Review A},
  year={2005},
  volume={71},
  pages={032333}
}
We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state extensions with appropriate properties and may be implemented as a semidefinite program. The main result of this work is to show that there is a series of tests of this kind such that if a multiparty state is entangled this will eventually be detected by one of the… 
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References

SHOWING 1-10 OF 38 REFERENCES
Distinguishing separable and entangled states.
TLDR
This work shows how to design families of operational criteria that distinguish entangled from separable quantum states, and provides an explicit construction of the corresponding entanglement witnesses.
Optimal teleportation with a mixed state of two qubits.
We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication such as to maximize the fidelity of teleportation
Three qubits can be entangled in two inequivalent ways
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single
Separability and Distillability of Multiparticle Quantum Systems
We present a family of 3-qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a
Complete family of separability criteria
We introduce a family of separability criteria that are based on the existence of extensions of a bipartite quantum state rho to a larger number of parties satisfying certain symmetry properties. It
Symmetric extensions of quantum States and local hidden variable theories.
TLDR
A simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states based on constructing a so-called symmetric quasiextension of the quantum state that gives rise to a localhidden variable model with a certain number of settings for the observers Alice and Bob.
Detecting quantum entanglement
The parts determine the whole in a generic pure quantum state.
TLDR
It is shown that almost every pure state of multiparty quantum systems is completely determined by the state's reduced density matrices of a fraction of the parties.
Reflections upon separability and distillability
An abstract formulation is presented of the so-called Innsbruck-Hannover programme that investigates quantum correlations and entanglement in terms of convex sets. A unified description is given of
Remarks on a quantum state extension problem
The problem is considered of finding, for a given pair of states on C*-algebras A1 ⊗ A2 and A2 ⊗ A3, a joint extension to A1 ⊗ A2 ⊗ A3. The fact that, in contrast to classical probability, such an
...
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