Bell theorem showed that under certain constraints, correlations impossible to attain by a classical system are instead allowed for quantum mechanics.
This notion, beside the profound theoretical implications became one of the fundamental tool in quantum information processing and a powerful resource for cryptographic protocols whose security can now be based only on the validity of physical laws, without any assumption on the
device used nor on the computational power of the adversary.
Although this phenomenon is not limited to the Bell's original scenario, until recently, very few different scenarios were explored in the literature.
This was due both to the absence of a unifying framework, and to the complexity of the task of characterizing the classical and quantum space of allowed distributions.
Recently a promising approach was introduced which employs causal modelling to study the constraints on observable correlations.
The aim of this project is to explore various promising causal scenarios to find novel kind of non-classicality, employing machine learning techniques to characterize efficiently the space of allowed correlations, and to identify new resources for cryptographic applications.
The classical causal modelling approach, together with its natural
quantum extension [1-2], represents a very promising route to achieve a
broad understanding of the non-classicality in general causal scenarios
and the notion of causality in quantum mechanics.
Being a very recent approach, it is not a surprise that, with very few exceptions,
the only causal scenario that has received attention for its remarkable quantum
non-locality effects is the Bell scenario.
In this context our aim is to exploit the bayesian network framework to explore previously
unknown quantum effects arising as consequence of different causal constraint.
This serves three different goals:
1) The first is extending our knowledge on the possible violations of classicality
admitted by quantum mechanics, which could help us to classify and find the general features
needed by a causal structure to admit non-classicality, and get a coherent picture on
the correlations under causal constraints.
2) The second is to provide novel resource for cryptographic protocols,
corroborated by experimental proof of principles, that do not require
a full-fledged loophole-free Bell test to be implemented, but can be
realized with more manageable technological requirements, while still
providing reasonable device-independent security.
3) The last is to prove that machine learning techniques can be a sound tool to tackle the problem of characterization of non-classicality, showing how powerful can be the interplay between these technologies and quantum information.
[1]: C. Brukner, Nature Physics 10.4 (2014): 259.
[2]: F. Costa, and S. Shrapnel. New Journal of Physics 18.6 (2016): 063032.