# Two-setting Bell inequalities for graph states

@article{Tth2006TwosettingBI, title={Two-setting Bell inequalities for graph states}, author={G{\'e}za T{\'o}th and Otfried Guehne and Hans J. Briegel}, journal={Physical Review A}, year={2006}, volume={73}, pages={022303} }

We present Bell inequalities for graph states with a high violation of local realism. In particular, we show that there is a basic Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of 2. This inequality needs the measurement of, at most, two operators for each qubit and involves only some of the qubits. We also show that for some families of graph states composite Bell inequalities can be constructed such that the violation of local realism…

## 34 Citations

Scalable Bell Inequalities for Qubit Graph States and Robust Self-Testing.

- Physics, Computer SciencePhysical review letters
- 2020

A general construction of Bell inequalities that are maximally violated by the multiqubit graph states and can be used for their robust self-testing, and numerical results indicate that the self- testing statements for graph states derived from the inequalities tolerate noise levels that are met by present experimental data.

Nonlocality for graph states

- Mathematics
- 2008

The possibility of preparing two-photon entangled states encoding three or more qubits in each photon leads to the following problem: If n quabits were distributed between two parties, which quantum…

Generalized Ardehali-Bell inequalities for graph states

- Physics
- 2008

We derive Bell inequalities for graph states by generalizing the approach proposed by Ardehali [Phys. Rev. A 46, 5375 (1992)] for Greenberger-Horne-Zeilinger (GHZ) states. Using this method, we…

Bell correlations at finite temperature

- PhysicsQuantum
- 2018

We show that spin systems with infinite-range interactions can violate at thermal equilibrium a multipartite Bell inequality, up to a finite critical temperature Tc. Our framework can be applied to a…

Qudit hypergraph states and their properties

- Mathematics, Physics
- 2018

Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing non-local properties and have promising applications in quantum information science and…

Detecting nonlocality of noisy multipartite states with the Clauser-Horne-Shimony-Holt inequality

- Physics
- 2014

The Clauser-Horne-Shimony-Holt inequality was originally proposed as a Bell inequality to detect nonlocality in bipartite systems. However, it can also be used to certify the nonlocality of…

Compact Bell inequalities for multipartite experiments

- Physics
- 2013

A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell…

Multipartite entanglement in XOR games

- Computer Science, MathematicsQuantum Inf. Comput.
- 2013

It is shown that the multipartite entangled states that are most often seen in today's literature can only lead to a bias that is a constant factor larger than the classical bias, which has the following surprising consequence: classical three-player XOR games do not follow an XOR parallel repetition theorem, even a very weak one.

The generation of a regular dodecahedron graph state with a superconducting qubit network

- Computer Science
- 2007

An improved architecture for the physical implementation of two-qubit operations between arbitrary pairs of qubits by current biasing of coupled Josephson junctions is proposed and a simple scheme for generating the graph states via the improved architecture is investigated.

## References

SHOWING 1-10 OF 41 REFERENCES

Bell inequalities for graph states.

- Mathematics, PhysicsPhysical review letters
- 2005

A family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states are derived, showing that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits.

Multiparty entanglement in graph states

- Physics
- 2004

Graph states are multiparticle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions.…

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

- Physics
- 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…

Experimental violation of a cluster state bell inequality.

- Physics, MedicinePhysical review letters
- 2005

It is experimentally demonstrate that correlations in a four-qubit linear cluster state cannot be described by local realism, and a cluster-state Bell parameter of 2.59+/-0.08 is observed, which is more than 7sigma larger than the threshold of 2 imposed byLocal realism.

All the Bell Inequalities

- Mathematics, Physics
- 1998

Bell inequalities are derived for any number of observers, any number of alternative setups for each one of them and any number of distinct outcomes for each experiment. It is shown that if a…

Optimal tests of quantum nonlocality

- Physics
- 2001

We present a general method for obtaining all Bell inequalities for a given experimental setup. Although the algorithm runs slowly, we apply it to two cases. First, the Greenberger-Horne-Zeilinger…

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

- Physics
- 2002

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…

Nonlocality of cluster states of qubits

- Physics
- 2005

We investigate cluster states of qubits with respect to their nonlocal properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it…

Bell inequalities and entanglement

- Computer Science, PhysicsQuantum Inf. Comput.
- 2001

The relation between Bell inequality violations and entanglement properties currently discussed in quantum information theory is discussed and maximal violations of Bell inequalities as well as states not violating (certain) Bell inequalities are investigated.