Dear Editor,

we would like to respond to the editorial decision on lack of suitability for
publication in Physical Review Letters of our manuscript XD10067L on probing
the quantum-classical boundary with a compression software. 

First, we appreciate the detailed comments at the editorial level, as they
helped us to hopefully improve the manuscript (we updated the corresponding
files in the submission system), but would like to contest the assertions
presented in the initial review that led to a rejection from even sending the
manuscript out to reviewers.

Let us start with the main problem you identified, namely that we did not
present a convincing case that this measure of quantumness is superior to
others (we believe you refer, apart from a Bell test, to the many measures
presented that assess entanglement). The major difference to the measure we
present compared to most of the others we are aware of is a non-statistical
approach; this means, we do not require the assumption of independent identical
distributions in an ensemble of realizations we observe, but we look at the
distribution as a whole. We would consider an assessment method that requires
less assumptions as superior, although we made no and do not whish to make a
judging comparison to others. To perhaps make this more clear, we now also
mention the absence of i.i.d. both in the description of a statistical
approach, and in the summarizing discussion at the end of the manuscript. We
do believe this is a significant step, and it holds in a somewhat staple
experiment on measurement of entangled photon pairs.

The novelty of this approach certainly was convincing enough to inspire work
by others (see Wolf, arxiv:1505:07037 ) already from the arxive version of the
manuscript; there, Stefan Wolf presented a viewpoint on non-locality that does
not even require counterfactual reasoning.

We do believe we carried out the suggested careful review of existing
literature, and found most relevant work on entropic Bell inequalities that
seem to cover a similar ground, and we believe we cite them accordingly (work
by Fuchs, Braunstein, Caves; our references 7,14 in the new manuscript
version). Although we don't know what existing literature reference the
comment was meant to address, we believe the large body of work on entanglement
measures like entanglement of formation, tangle, offer quantitative measures,
but do not really remove one of the basic assumptions. We therefore feel that
we at least would like to know if we missed a major development. A
generalization to more complex states, although interesting and already
explored by colleagues who work on such systems, seems a bit of an odd
requirement for the introduction of a new concept in a manuscript.

We now like to address the other issues raised in the editorial
response. First, the comment on the Church-Turing hypothesis, and our
reference to controversial work of Stephen Wolfram (old reference 7). The
point we want to make in this work does actually not require big
interpretations about the meaning of simulatability of different systems, and
we certainly do not want to sell a hypothesis as a proof. The mentioning of
these ideas were merely there to hint at a discussion in perhaps a similar
spirit. We did remove the controversial reference, and stick now to a strict
statement of facts. As it was probably distracting and perhaps putting the
work in a light we did not intend, we also removed the comment (and associated
discussion) on complexity classes P,NP in the summarizing sections of the old
manuscript, as we just used them to indicate that perhaps a wider view of
complexity of systems would be a worthy endeavor.

We also believe that we did not make a claim that our experimental observation
supports the hypothesis that the compression method is a universal
tool. However, within the limits we explicitly state (mostly that the Kolmogorov
complexity can be reasonably well approximated by the compressibility of a
data set), we stand by our claim that the data at hand violates the inequality
we present, and hence can not be reproduced by local Universal Turing
Machines. We do believe that, if this method works also for other physical
systems, it would offer an interesting alternative, but did not and do not
make a general claim. We reformulated the concluding paragraph to make this
even more explicit than it was before.

In summary, we feel that the main criticism expressed in the editorial
assessment was perhaps triggered by us not making these points clear enough,
and hope that we have addressed them better with the revised manuscript.

We feel that the idea of compressibility as a measure of non-classicality of a
system has potential of opening a new field in physics (as one of the criteria
for a paper to be considered for publication in PRL ) - first indications are
works that make already references to our work, and colleagues trying to use
these methods to assess more complex quantum systems in atomic physics. The
presented method is superior to existing ones we are aware of in the sense
that it does not require an i.i.d. assumption.

We therefore would like to ask you to reconsider the updated manuscript as a
publication in Physical Review Letters. If you feel that the changes we made
to introduction and summary in this manuscript were substantial enough to
warrant a new submission rather than an update of the existing one, please do
let us know.

With Best Regards on behalf of all authors,

Christian Kurtsiefer