# 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 } }

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…

## 36 Citations

### Bell inequality, separability and entanglement distillation

- Physics
- 2011

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.

- MathematicsPhysical review letters
- 2006

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.

- PhysicsPhysical review letters
- 2005

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

- Mathematics
- 2003

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.

- PhysicsNature communications
- 2014

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

- Mathematics
- 2017

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.

- PhysicsPhysical review letters
- 2012

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

- Physics
- 2008

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

- Physics
- 2006

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

- Mathematics, Physics
- 2007

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.

- PhysicsPhysical review letters
- 2001

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?

- Physics
- 1998

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

- Mathematics
- 1999

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.

- PhysicsPhysical review letters
- 1995

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

- Mathematics
- 2001

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

- Physics
- 1997

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

- Physics
- 1998

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…