Keywords: Nonlocal games, Nonlocal boxes, Communication complexity.

Communication complexity quantifies how difficult is a Boolean function $f(X, Y)$ to be computed by two distant parties, Alice and Bob, knowing that each party receives only half of the inputs, and under the constraint of communicating as few bits as possible [Yao79, KN96].
In some rare cases, only one bit of communication is enough to evaluate $f$, in which case we say that communication complexity collapses, see the following figure:

Previous image from [BBP23].
It would be very surprising to find in Nature a resource that collapses communication complexity for any Boolean function $f$ with arbitrary entry size, since it would be too powerful to being able to correctly estimate the value of any Boolean function with only one bit of communication.

Previous image from [BBCNP23].
Interestingly, it is known that the famous PR box is collapsing, and even some of its noisy approximations.
On the opposite, it is also known that quantum correlation cannot collapse communication complexity (and even the "almost quantum correlations").
To that day, the question is still open whether the remaining non-signalling boxes are collapsing, there is still a gap to be filled.
See more details in [MSc. thesis].

Previous image from [BBP23].
In our work, we reduce the unknown gap by finding new nonlocal boxes that collapse communication complexity, see our articles.

My supervisors

My supervising team is composed of three complementary perspectives of Quantum Information Theory:

Anne Broadbent (University of Ottawa), expert in quantum cryptography, quantum nonlocality and quantum complexity theory.
See the quantum team in Ottawa.

Ion Nechita (CNRS, University of Toulouse), expert in random matrix theory, with a recent focus on the theory of random tensors, and in the theory of quantum entanglement.