# Bell’s inequalities and distillability in N -quantum-bit systems

@article{Acn2002BellsIA, title={Bell’s inequalities and distillability in N -quantum-bit systems}, author={A. Ac{\'i}n and V. Scarani and M. Wolf}, journal={Physical Review A}, year={2002}, volume={66} }

The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and… Expand

#### 26 Citations

Asymptotic violation of Bell inequalities and distillability.

- Mathematics, Physics
- Physical 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. Expand

Bound entanglement maximally violating Bell inequalities: Quantum entanglement is not fully equivalent to cryptographic security

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- 2006

It is shown that Smolin four-qubit bound entangled states [J. A. Smolin, Phys. Rev. A 63, 032306 (2001)] can maximally violate the simple two-setting Bell inequality similar to the standard… Expand

Violations of Bell inequalities as lower bounds on the communication cost of nonlocal correlations

- Physics
- 2003

To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality… Expand

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- Mathematics
- 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… Expand

A relevant two qubit Bell inequality inequivalent to the CHSH inequality

- Mathematics, Physics
- 2004

We computationally investigate the complete polytope of Bell inequalities for two particles with small numbers of possible measurements and outcomes. Our approach is limited by Pitowsky's connection… Expand

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

- 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… Expand

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… Expand

THE CHSH-TYPE INEQUALITIES FOR INFINITE-DIMENSIONAL QUANTUM SYSTEMS

- Mathematics, Physics
- 2013

By establishing CHSH operators and CHSH-type inequalities, we show that any entangled pure state in infinite-dimensional systems is entangled in a 2⊗2 subspace. We find that, for infinite-dimensional… Expand

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… Expand

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- Physics, Medicine
- Physical review letters
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A method is provided to generate systematically bound entangled quantum states which can still be used for steering and, therefore, to rule out local hidden state models and sheds light on the relations between the various views on quantum correlations. Expand