Katherine A. Maxwell

Publications

  • The Super Mumford Form and Sato Grassmannian. Preprint
  • arXiv:2002.06625

    We describe a supersymmetric generalization of the construction of Kontsevich and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our main result is the existence of a flat holomorphic connection on the line bundle λ3/2⊗λ−51/2 on the moduli space of triples: a super Riemann surface, a Neveu-Schwarz puncture, and a formal coordinate system.
  • Bell Inequalities with Communication Assistance. with E. Chitambar
  • K. Maxwell and E. Chitambar, Bell Inequalities with Communication Assistance. Phys. Rev. A, 89, 042108. (15 April 2014).

    arXiv:1405.3211DOI

    In this paper we consider the possible correlations between two parties using local machines and shared randomness with an additional amount of classical communication. This is a continuation of the work initiated by Bacon and Toner in Ref. [Phys. Rev. Lett. 90, 157904 (2003)] who characterized the correlation polytope for 2×2 measurement settings with binary outcomes plus one bit of communication. Here, we derive a complete set of Bell Inequalities for 3×2 measurement settings and a shared bit of communication. When the communication direction is fixed, nine Bell Inequalities characterize the correlation polytope, whereas when the communication direction is bi-directional, 143 inequalities describe the correlations. We then prove a tight lower bound on the amount of communication needed to simulate all no-signaling correlations for a given number of measurement settings.

Research Interests

My interests include mathematical physics, supergeometry, and algebraic geometry. More specifically, I have been working with Lie algebroids, super Riemann surfaces, determinant line bundles, infinite dimensional geometries, moduli space of curves, and the Sato Grassmannian.

As an undergraduate, I worked on theoretical quantum mechanics research, first from the perspective of quantum information theory investigating entanglement with Eric Chitambar, and second in a project interpreting Wigner functions as the time components of a particle current with Taner Edis.