Francesca La Piana

• Piana, Francesca La & Müller-Hermes, Alexander (2026). Annihilating and breaking Lorentz cone entanglement. Linear Algebra and its Applications. ISSN 0024-3795. 739, p. 68–103. doi: 10.1016/j.laa.2026.03.012. Full text in Research Archive Show summary

  Linear maps between finite-dimensional ordered vector spaces with orders induced by proper cones CA and CB are called entanglement breaking if their partial application sends the maximal tensor product K⊗maxCA into the minimal tensor product K⊗minCB for any proper cone K. We study the larger class of Lorentz-entanglement breaking maps where K is restricted to be a Lorentz cone of any dimension, i.e., any cone over a Euclidean ball. This class of maps appeared recently in the study of asymptotic entanglement annihilation and it is dual to the linear maps factoring through Lorentz cones. Our main results establish connections between these classes of maps and operator ideals studied in the theory of Banach spaces. For operators u:X→Y between finite-dimensional normed spaces X and Y we consider so-called central maps which are positive with respect to the cones CA=CX and CB=CY. We show how to characterize when such a map factors through a Lorentz cone and when it is Lorentz-entanglement breaking by using the Hilbert-space factorization norm γ2 and its dual γ2⁎. We also study the class of Lorentz-entanglement annihilating maps whose local application sends the Lorentzian tensor product CA⊗LCA into the minimal tensor product CB⊗minCB. When CA is a cone over a finite-dimensional normed space and CB is a Lorentz cone itself, the central maps of this kind can be characterized by the 2-summing norm π2. Finally, we prove interesting connections between these classes of maps for general cones, and we identify examples with particular properties, e.g., cones with an analogue of the 2-summing property.

• Piana, Francesca La & Morsella, Gerardo (2025). The Fermionic Massless Modular Hamiltonian. Communications in Mathematical Physics. ISSN 0010-3616. 406. doi: 10.1007/s00220-025-05253-1. Full text in Research Archive Show summary

  We provide an explicit expression for the modular hamiltonian of the von Neumann algebras associated to the unit double cone for the (fermionic) quantum field theories of the 2-component Weyl (helicity 1/2) field, and of the 4-component massless Dirac and Majorana fields. To this end, we represent the one particle spaces of these theories in terms of solutions of the corresponding wave equations, and obtain the action of the modular group on them. As an application, we compute the relative entropy between the vacuum of the massless Majorana field and one particle states associated to waves with Cauchy data localized in the spatial unit ball.

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• Piana, Francesca La (2026). Operator Algebras and Convex Geometry in Quantum Theory: Modular Theory, Convex Cones, and Quantum Symmetries. Universitetet i Oslo. Full text in Research Archive Show summary

  Quantum theory describes the behaviour of physical systems at the microscopic scale. It is also the foundation of quantum information theory, where one studies how information can be stored, transmitted, and processed using quantum systems. My thesis does not focus on the experimental side of quantum theory. Instead, it studies the mathematical structures behind it, using tools from operator algebras, convex geometry, and quantum information theory. The thesis is a collection of three papers, each addressing a different aspect of these structures. The first paper belongs to algebraic quantum field theory. It studies the localization of certain quantum fields in bounded regions of Minkowski spacetime. The main result is an explicit description of the modular Hamiltonian for free massless fermions. The second paper studies Lorentz entanglement-breaking maps, a class of maps related to entanglement. The main results connect these maps and related Lorentz-factorizable maps with operator ideals from Banach space theory. The third paper studies a quantum version of the Birkhoff–von Neumann theorem with graph constraints. One of the main results shows that the theorem already fails for the square graph. The paper also studies graph quantum magic squares from a geometric point of view, showing that they form free spectrahedra.

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