Large Violation of Bell Inequalities with Low Entanglement
By Marius Junge, Carlos Palazuelos. 2010
141 citations recorded by the source corpus.
In this paper we obtain violations of general bipartite Bell inequalities of order $${\frac{\sqrt{n}}{\log n}}$$ with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/71f92e8f5fee9ecea7e30034f0155b916eb7b860
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Gilles Pisier
- Marius Junge
- Carlos Palazuelos
- David Pérez-García
- Miguel Navascués
- Volkher B. Scholz
- Reinhard F. Werner
- John Watrous
In Atomic and Molecular Physics, and Optics
- Gilles Pisier
- Marius Junge
- Carlos Palazuelos
- David Pérez-García
- Miguel Navascués
- Volkher B. Scholz
- Reinhard F. Werner
- John Watrous
In Computational Theory and Mathematics
Citations in the corpus
- Tensor Products of C*-Algebras and Operator Spaces (2020, background): “See [139, 140] for more recent information on Bell’s inequalities and their connections with operator spaces.”
- Connes' embedding problem and Tsirelson's problem (2010, methodology): “In [12] the authors showed that this order is very important in the context of violation of Bell inequalities.”
- Grothendieck's Theorem, past and present (2011, background): “For more information on the connection between Grothendieck’s and Bell’s inequalities, see [81, 1, 36, 20, 69, 62, 141, 140].”