Dear Editor,

please find enclosed a manuscript on a combined theoretical/experimental work on a what we believe is a new approach to assess the quantumness of a physical system. While the combination of quantum physics with computer science led to the emergence of many ideas how to possibly do some useful computation using quantum physics, there have been many exciting inspirations to traditional physics as well.

In the combined theoretical and experimental work we present in this manuscript, we tried to use very elementary computer science concepts like the compressibility of data sets to evaluate the "quantumness" of a real physical system. We find that this plan seems to work, at least for  a maximally entangled bipartite system, in the sense that the equivalent of an entropic Bell inequality can be tested and found violated with relatively simple computational tools applied to measured data.

The present manuscript is in part a follow-up of an earlier submission to PRL (reference LN13405) from about a year ago, which was not further pursued because also the opportunity to do an experiment came up in the mean time. The manuscript at hand is completely rewritten, and covers substantially new material - on one hand, we could make the theoretical development of the idea much more succinct and thereby accessible to a wider audience. On the other hand, we were able to directly demonstrate the idea in an experiment - with existing compressors, making the whole idea of an algorithmic description of non-classicality of systems much more specific.

We also feel that we needed to add an additional technical analysis of how we evaluated several compression algorithms for their suitability - this is important for the practical experiment, but really too technical to justify inclusion in the main part of the paper, and we moved it into a supplementary material file. We do hope that this meets the publication style in Physical Review Letters.

To us, this looks like a funny combination of computer science and quantum physics that may even help to "understand" entanglement not only in a statistical, but perhaps algorithmic way. As this aspect may have reasonably far reaching consequences, and we used openly available compression algorithms for this demonstration, we feel that Physical Review Letters may just be a very suitable platform to present this work to a wide audience of physicists.

We therefore would kindly ask you to consider a publication in PRL. 

With Best Regards on behalf of all authors,

Dagomir Kaszlikowski and Christian Kurtsiefer