Welcome on Pierre's personal page 

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Hey there! My name is Pierre Botteron and I'm a third-year PhD student at the University of Toulouse (France) and at the University of Ottawa (Canada). My field of research is Quantum Information Theory, from a math perspective, and I work under the joint supervision of Anne Broadbent, Ion Nechita, and Clément Pellegrini—see details below.

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Research Interests

  Articles   Talks & Posters

We explore foundational aspects of quantum information theory and quantum cryptography.

Keywords:

• Nonlocal games,
• Communication complexity,
• Quantum cryptography.

Foundations of QIT: We investigate quantum correlations in interactive settings, including the CHSH and graph isomorphism games. We aim to distinguish quantum correlations from non-signaling correlations by leveraging the principle of communication complexity. To this end, we employ techniques such as distributed computation, majority-function-based distillation protocols, the algebraic and geometric properties of nonlocal box wirings, and variations of some graph properties such as isomorphism, transitivity, and equitable partitions. This inquiry advances our understanding of non-physical correlations.

Quantum Cryptography: We address a key open problem in cryptography: the feasibility of unclonable encryption. We aim to construct an encryption scheme that prevents two distant parties from simultaneously obtaining information about a shared encrypted message. We introduce a candidate for unclonable encryption in the plain model, i.e. without assumptions, in working towards an unconditional proof. Our protocol is based on Clifford algebra, utilizing complex Hermitian unitary matrices that anti-commute. For small key sizes, we rigorously prove security using sum-of-squares methods, while for larger key sizes, we provide strong numerical evidence via the NPA hierarchy.

  More details

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PhD Supervisors

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

• Anne Broadbent (University of Ottawa), an expert in quantum cryptography, quantum nonlocality, and quantum complexity theory. See the quantum team in Ottawa.
• Ion Nechita (CNRS, University of Toulouse), an expert in random matrix theory, with a recent focus on the theory of random tensors, and in the theory of quantum entanglement.
• Clément Pellegrini (University of Toulouse), an expert on stochastic aspects of quantum mechanics, with a focus on the theory of quantum trajectories and open quantum systems. See the quantum team in Toulouse.

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