My work is focused on categorical and algebraic structures with applications to quantum information theory.
- Reference frame-independent quantum protocols, with Jamie Vicary:
- 'Perfect tight quantum teleportation without a shared reference frame.' (https://arxiv.org/abs/1710.01060). For reference frames with finitely many configurations, we show that perfect teleportation may often be achieved with no communication of reference frame information. Our approach uses algebraic structures called 'equivariant unitary error bases', which we classify for qubits. (A very early version of this work appeared in the proceedings of QPL 2016 as 'Tight reference frame independent quantum teleportation'.)
- 'Quantum teleportation with infinite reference frame uncertainty.' (https://arxiv.org/abs/1802.09040). Provides 'perfect' and 'tight' teleporation schemes for reference frames with infinitely many configurations.
- Higher dimensional algebra:
- Quantum functions, with Benjamin Musto and David Reutter:
- 'A compositional approach to quantum functions.' (https://arxiv.org/abs/1711.07945). Unites various notions of quantum function and quantum bijection within a single 2-categorical framework.
- 'The Morita theory of quantum graph isomorphisms.' (https://arxiv.org/abs/1801.09705). We apply the 2-categorical framework developed in the previous paper to develop a classification of quantum graph isomorphisms with applications to quantum pseudo-telepathy.