Bounding the set of quantum correlations.

@article{Navascus2007BoundingTS,
  title={Bounding the set of quantum correlations.},
  author={Miguel Navascu{\'e}s and Stefano Pironio and Antonio Ac{\'i}n},
  journal={Physical review letters},
  year={2007},
  volume={98 1},
  pages={
          010401
        }
}
We introduce a hierarchy of conditions necessarily satisfied by any distribution P_{alphabeta} representing the probabilities for two separate observers to obtain outcomes alpha and beta when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Among other applications, our approach can be used to obtain upper bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the… 
Simple conditions constraining the set of quantum correlations
The characterization of the set of quantum correlations in Bell scenarios is a problem of paramount importance for both the foundations of quantum mechanics and quantum information processing in the
Bell inequalities for three systems and arbitrarily many measurement outcomes
We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin-Bell inequality. For a small number of outcomes,
Tripartite quantum state violating the hidden-influence constraints
The possibility to explain quantum correlations via (possibly) unknown causal influences propagating gradually and continuously at a finite speed v>c has attracted some attention recently. In
Bounding sets of sequential quantum correlations and device-independent randomness certification
TLDR
This work shows how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements.
Monogamy of non-local quantum correlations
  • B. Toner
  • Computer Science
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2008
TLDR
This work bound the trade-off between AB's and AC's violation of the Clauser–Horne–Shimony–Holt inequality and demonstrates that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.
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
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.
Computational perspectives on Bell Inequalities and many-body quantum correlations
The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems
A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
TLDR
It is shown that in some cases it is possible to conclude that a given set of correlations is quantum after performing only a finite number of tests, and used in particular to bound the quantum violation of various Bell inequalities.
Quantum Bell inequalities from Information Causality – tight for Macroscopic Locality
TLDR
This work presents a family of inequalities, which approximate the set of quantum correlations in Bell scenarios where the number of settings or outcomes can be arbitrary, and derives these inequalities from the principle of Information Causality, and thus does not assume the formalism of quantum mechanics.
...
...

References

SHOWING 1-8 OF 8 REFERENCES
Found
  • C. Ross
  • Medicine
    The Dental register
  • 1869
Phys
  • Rev. A 73, 022110
  • 2006
Speakable and Unspeakable in Quantum Mechanics
Phys
  • Rev. Lett. 95, 010503
  • 2005
Phys
  • Rev. Lett. 97, 170409 (2006). PRL 98, 010401
  • 2007
in Symposium on the Foundations of Modern Physics
  • edited by P. Lahti and P. Mittelstaedt
  • 1985