# Communication Strength of Correlations Violating Monogamy Relations

## Abstract

In any theory satisfying the no-signaling principle correlations generated among spatially separated parties in a Bell-type experiment are subject to certain constraints known as monogamy relations. Recently, in the context of the black hole information loss problem it was suggested that these monogamy relations might be violated. This in turn implies that correlations arising in such a scenario must violate the no-signaling principle and hence can be used to send classical information between parties. Here, we study the amount of information that can be sent using such correlations. To this aim, we first provide a framework associating them with classical channels whose capacities are then used to quantify the usefulness of these correlations in sending information. Finally, we determine the minimal amount of information that can be sent using signaling correlations violating the monogamy relation associated to the chained Bell inequalities.

## Keywords

Monogamy relations No-signaling principle Capacities of communication channels## Notes

### Acknowledgments

We thank M. Horodecki, R. Horodecki, P. Kurzyński, M. Lewenstein, J. Łodyga and A. Wójcik for helpful discussions. W. K. and A. G. were supported by the Polish Ministry of Science and Higher Education Grant no. IdP2011 000361. M. O. was supported by the ERC Advanced Grant QOLAPS, START scholarship granted by Foundation for Polish Science, the Polish National Science Centre grant under Contract No. DEC-2011/01/M/ST2/00379, the John Templeton Foundation, the Spanish MINECO grant FOQUS, the “Severo Ochoa” Programme (SEV-2015-0522), and the Generalitat de Catalunya grant SGR875. R. A. was supported by the ERC Advanced Grant OSYRIS, the EU IP SIQS, the John Templeton Foundation, the Spanish Ministry project FOQUS (FIS2013-46768) and the Generalitat de Catalunya project 2014 SGR 874. W. K. thanks the Foundation of Adam Mickiewicz University in Poznań for the support from its scholarship programme. A.G. thanks ICFO–Institut de Ciències Fotòniques for hospitality.

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