Dear Editor,

please find enclosed a manuscript on an experiment on reaching Tsirelson's bound in a photon pair experiment. There has been amazing progress in photon pair experiments on testing Bell inequalities in the recent past, both in quality of the entangled states prepared from various sources, and in the detection efficiency.

We tried to find out how close we can come to the quantum prediction of the degree of violation of a CHSH-type Bell inequality. A limitation for this is the bound was proven by Tsirelson in 1980 to be exactly 2 sqrt 2 or 2.828427...


There has been a recent prediction by A. Grinbaum that, based on an informational definition of an Observer, there is an upper bound to the degree of violation of 2.82537 if quantum physics were not fundamental, and there would be a deeper theory that is effectively approximated by quantum physics.

In the work we present in the manuscript, we find that we exceed this bound presented by Grinbaum by about 2.7 standard deviations - and that the violation we observe (2.8276+-0.00082) is compatible with reaching the Tsirelson bound. To our knowledge, this experiment approaches the Tsirelson bound with the lowest uncertainty ever reported, over an order of magnitude better than the best result reported before by two different groups.

Our result has important consequences for cryptographic security in a device-independent scenario, or when certifying the amount of randomness contained in measurements on entangled systems, as a higher the violation of a Bell inequality leads to a larger the amount of certified randomness.

We believe that in the light of the violation of Grinbaum's bound, this work is not only a substantial technical advance of a by now traditional observation of the violation of a CHSH Bell-type inequality, but has important enough consequences on the validity of quantum physics to  be interesting to the wide audience of Nature Physics and would like to consider it for publication.

With Best Regards on behalf of all authors,

Christian Kurtsiefer