Distillability, bell inequalities, and multiparticle bound entanglement.

@article{Acn2002DistillabilityBI,
  title={Distillability, bell inequalities, and multiparticle bound entanglement.},
  author={Antonio Ac{\'i}n},
  journal={Physical review letters},
  year={2002},
  volume={88 2},
  pages={
          027901
        }
}
  • A. Acín
  • Published 7 August 2001
  • Physics
  • Physical review letters
We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, Dür [Phys. Rev. Lett. 87, 230402 (2001)] has shown that there are some multiparticle bound entangled states which are nonseparable and nondistillable, that violate a Bell inequality. We prove that for all the states violating this inequality there exists at least one splitting of the parties into two groups such that some pure-state entanglement can be distilled, obtaining a… 

Bell inequality, separability and entanglement distillation

In this review, we introduce well-known Bell inequalities, the relations between the Bell inequality and quantum separability, and the entanglement distillation of quantum states. It is shown that

Asymptotic violation of Bell inequalities and distillability.

TLDR
It is shown that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups.

Multipartite entanglement inequalities via spin vector geometry.

TLDR
In inequalities for multipartite entanglement, derived from the geometry of spin vectors, are introduced, which are violated by certain bound entangled states for which no Bell-type violation has yet been found.

LETTER TO THE EDITOR: Violation of Bell's inequalities and distillability for N qubits

We consider quantum systems composed of N qubits, and the family of all Bell's correlation inequalities for two two-valued measurements per site. We show that if an N-qubit state ρ violates any of

Disproving the Peres conjecture by showing Bell nonlocality from bound entanglement.

TLDR
The Peres conjecture is disproved by showing that an undistillable bipartite entangled state--a bound entangled state)--can violate a Bell inequality, which implies neither entanglement distilling, nor non-positivity under partial transposition.

Family of Bell inequalities violated by higher-dimensional bound entangled states

We construct ($d\times d$)-dimensional bound entangled states, which violate, for any $d>2$, a bipartite Bell inequality introduced in this paper. We conjecture that the proposed class of Bell

Quantum nonlocality does not imply entanglement distillability.

TLDR
This work presents analytically a 3-qubit entangled state that is separable along any bipartition, and implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled.

A witness of multipartite entanglement strata

We describe an entanglement witness for N-qubit mixed states based on the properties of N-point correlation functions. As the degree of violation increases beyond different threshold values, or

Generalized Smolin states and their properties

Four-qubit bound entangled Smolin states are generalized with help of the Hilbert-Schmidt formalism to any even number of qubits. They are shown to maximally violate simple correlation Bell

Multipartite positive-partial-transpose inequalities exponentially stronger than local reality inequalities

We show that positivity of every partial transpose of $N$-partite quantum states implies inequalities on Bell correlations which are stronger than standard Bell inequalities by a factor of

References

SHOWING 1-10 OF 67 REFERENCES

Multipartite bound entangled states that violate Bell's inequality.

  • W. Dür
  • Physics
    Physical review letters
  • 2001
TLDR
It is proved that there exist multipartite bound entangled states (i.e., nonseparable, nondistillable states) that violate a multipartsite Bell inequality, which implies that (i) violation of Bell's inequality is not a sufficient condition for distillability and (ii) some bound entangledStates cannot be described by a local hidden variable model.

Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?

It is shown that if a mixed state can be distilled to the singlet form it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two

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

Bell's Inequalities and Density Matrices: Revealing "Hidden" Nonlocality.

  • Popescu
  • Physics
    Physical review letters
  • 1995
TLDR
For mixed states, correlations arising from a single ideal measurement on each system may obey standard Bell inequalities, yet when each system is subjected to a sequence of ideal measurements the correlations are nonlocal.

All-multipartite Bell-correlation inequalities for two dichotomic observables per site

We construct a set of ${2}^{{2}^{n}}$ independent Bell-correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are

Inseparable Two Spin- 1 2 Density Matrices Can Be Distilled to a Singlet Form

A quantum system is called inseparable if its density matrix cannot be written as a mixture of product states. In this Letter we apply the separability criterion, local filtering, and Bennett et al.

Violation of Bell Inequalities by Photons More Than 10 km Apart

A Franson-type test of Bell inequalities by photons 10.9 km apart is presented. Energy-time entangled photon pairs are measured using two-channel analyzers, leading to a violation of the inequalities
...