A relevant two qubit Bell inequality inequivalent to the CHSH inequality

@article{Collins2004ART,
  title={A relevant two qubit Bell inequality inequivalent to the CHSH inequality},
  author={Daniel Geoffrey Collins and Nicolas Gisin},
  journal={Journal of Physics A},
  year={2004},
  volume={37},
  pages={1775-1787}
}
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 of this problem to the computationally hard NP problem. Despite this, we find that there are very few relevant inequivalent inequalities for small numbers. For example, in the case with three possible 2-outcome measurements on each particle, there is just one new inequality. We describe mixed 2… 

Figures from this paper

Quantum bounds on Bell inequalities
We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement
Bell inequalities with three ternary-outcome measurements - from theory to experiments
We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations
Efficiency of higher-dimensional Hilbert spaces for the violation of Bell inequalities
We have determined numerically the maximum quantum violation of over 100 tight bipartite Bell inequalities with two-outcome measurements by each party on systems of up to four dimensional Hilbert
Generalizing Optimal Bell Inequalities.
TLDR
This work develops a method to characterize Bell inequalities under constraints, which may be given by symmetry or other linear conditions, which allows one to search systematically for generalizations of given Bell inequalities to more parties.
Bounds on quantum correlations in Bell-inequality experiments
Bell-inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be
Entanglement estimation from Bell inequality violation
It is well known that the violation of Bell’s inequality in the form given by Clauser, Horne, Shimony, and Holt (CHSH) in two-qubit systems requires entanglement, but not vice versa, i.e., there are
Visualizing Two Qubits
The notions of entanglement witnesses and separable and entangled states for a two qubit system can be visualized in three dimensions using the SLOCC equivalence classes. This visualization preserves
Characterization of quantum correlations with local dimension constraints and its device-independent applications
TLDR
This work characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations and derives a Bell-type inequality that can only be violated when each of the three parties has local dimension greater than two.
Finding optimal Bell inequalities using the cone-projection technique
Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called
...
...

References

SHOWING 1-10 OF 24 REFERENCES
Optimal tests of quantum nonlocality
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
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
Clauser-Horne inequality for three-state systems
We show a new Bell-Clauser-Horne inequality for two entangled three-dimensional quantum systems (socalled qutrits). This inequality is not violated by a maximally entangled state of two qutrits
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.
Quantum communication between N partners and Bell's inequalities.
TLDR
It is demonstrated the existence of a link between the security of these protocols against individual attacks by the eavesdropper, and the violation of some Bell's inequalities, generalizing the link that was noticed some years ago for two-partners quantum cryptography.
On the Einstein-Podolsky-Rosen paradox
THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional
Local realism and measured correlations in the spin- s Einstein-Podolsky-Rosen experiment
Two aspects of the Clauser-Horne conditions for the compatibility with local realism of measured spin-\textonehalf{} Einstein-Podolsky-Rosen correlations are investigated in the spin-$s$ case. (1) A
...
...