Stephan Weispost-doctoral researcher at theCentre for Mathematics of the University of Coimbra Departamento de Matemática Universidade de Coimbra 3001 – 501 Coimbra Portugal office: 5.11 telephone: +351 239 791 170 e-mail: maths@weis-stephan.de |
• background I obtained a PhD in mathematics in 2009 from the University of Erlangen-Nuremberg, Germany, under supervision by Andreas Knauf. In 2011 I moved to Leipzig, Germany, to work with Arleta Szkoła and Nihat Ay at the Max Planck Institute for Mathematics in the Sciences. I was a post-doctoral researcher at the State University of Campinas, Brazil (2015-2016) and at the Ecole Polytechnique de Bruxelles, Belgium (2016-2018). • research mathematical physics, more specifically mathematical methods in quantum mechanics methods — convex geometry — matrix analysis topics — numerical ranges, quantum marginals — lattices of ground spaces — maximum-entropy states — quantum correlations — quantum coin flipping • internet profiles • arXiv • Google Scholar • ResearchGate • ResearcherID (Web of Science™) • ORCID • currículo lattes (CNPq, in Portuguese) • publications Accepted journal papers • I. M. Spitkovsky, S. Weis, Signatures of quantum phase transitions from the numerical range, Journal of Mathematical Physics, in press. About • arXiv The differential geometry of the boundary of the numerical range is related with ground state energy crossings of a one-parameter Hamiltonian, and with continuity of a maximum-entropy inference map. • S. Weis, A variational principle for ground spaces, Reports on Mathematical Physics, in press. About • arXiv A variational formula for ground spaces of a vector space of energy operators is derived from the geometry of normal cones of a state space. The theory is demonstrated with examples. Refereed journal papers 13) K. Szymański, S. Weis, K. Życzkowski, Classification of joint numerical ranges of three hermitian matrices of size three, Linear Algebra and its Applications 545 (2018), 148-173. About • arXiv • Journal link (open access) The joint numerical range of three 3x3 matrices is characterized in terms of its flat boundary portions (segments and filled ellipses). Examples are given for the ten possible three-dimensional objects. 12) S. Weis, Operator systems and convex sets with many normal cones, Journal of Convex Analysis 25 (2018), 41–64. About • arXiv • Journal link The state space of an operator system is ubiquitous in quantum mechanics. We study the lattice of its exposed faces, which is isomorphic to the lattice of ground spaces of the operator system. 11) I. M. Spitkovsky, S. Weis, Pre-images of extreme points of the numerical range, and applications, Operators and Matrices 10 (2016), 1043-1058. About • arXiv • Journal link Grünbaum's notion of poonem allows to compute pre-images of extreme points. A non-unique pre-image is then characterizable in terms of Hausdorff convergence of facets. An application is to describe closures of sets of 3x3 matrices whose numerical ranges have the same shape. 10) S. Weis, Maximum-entropy inference and inverse continuity of the numerical range, Reports on Mathematical Physics 77 (2016), 251-263. About • arXiv • Journal link (open access) Continuity of the maximum-entropy inference which refers to two quantum observables is proven equivalent to the inverse continuity of numerical range points. This yields a continuity condition depending on analytic eigenfunctions. 9) L. Rodman, I. M. Spitkovsky, A. Szkoła, S. Weis, Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach, Journal of Mathematical Physics 57 (2016), 015204. About • arXiv • Journal link We dwell on convex geometry (lower semi-continuity of the face function) to study the continuity of maximum-entropy states (and of correlations). We explore the case of two observables using pre-images of the numerical range. 8) S. Weis, A. Knauf, N. Ay, M.-J. Zhao, Maximizing the divergence from a hierarchical model of quantum states, Open Systems & Information Dynamics 22 (2015), 1550006. About • arXiv • SFI Working Paper • Journal link We discuss many-party quantum correlations and their maximizers. We point out differences to the correlations in probability distributions. 7) S. Weis, Continuity of the maximum-entropy inference, Communications in Mathematical Physics 330 (2014), 1263-1292. About • arXiv • MPI MIS Preprint • Journal link A continuity criterion is proven for the inference of the state of a finite-level quantum system under linear constraints. The set of inference states of the maximum-entropy inference is described. 6) S. Weis, Information topologies on non-commutative state spaces, Journal of Convex Analysis 21 (2014), 339-399. About • arXiv • MPI MIS Preprint • Journal link The Umegaki relative entropy defines topologies on the state space of an N-level quantum system. The rI-topology extends Pythagorean and projection theorems for exponential families. 5) S. Weis, A. Knauf, Entropy distance: New quantum phenomena, Journal of Mathematical Physics 53 (2012), 102206. About • arXiv • MPI MIS Preprint • Journal link New quantum features are presented: A discontinuous maximum-entropy inference and a discontinuous entropy distance for 3-level quantum systems. 4) S. Weis, Duality of non-exposed faces, Journal of Convex Analysis 19 (2012), 815-835. About • arXiv • MPI MIS Preprint • Journal link Galois connections relate faces and touching cones of a polar pair of convex bodies. In dimension two this gives a duality (up to multiplicity) between certain singular points and non-exposed points. 3) S. Weis, A note on touching cones and faces, Journal of Convex Analysis 19 (2012), 323-353. About • arXiv • Journal link Touching cones of a convex set, that is non-empty faces of normal cones, are explored. 2) S. Weis, Quantum convex support, Linear Algebra and its Applications 435 (2011), 3168-3188. About • arXiv • Journal link (open access) All faces, including the non-exposed faces, are calculated algebraically for projections of the state space of an N-level quantum system. The projections are convex duals of sections of the state space.
1) I. Voigt, S. Weis, Polyhedral Voronoi cells, Contributions to Algebra and Geometry 51 (2010), 587-598. About • arXiv • Journal link (open access) A Voronoi cell is defined in terms of a point set in Euclidean space. Several cones associated to the point set are used to decide if the cell is a polyhedron. Refereed conference papers 3) S. Weis, The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics, AIP Conference Proceedings 1641 (2015), 173-180. About • arXiv • Journal link We summarize geometric ideas about the `boundary' of a Gibbs family of finite-level quantum states. The `boundary' consists of ultra cold quantum states. We prove a zero-temperature representation of the irreducible correlation. 2) S. Weis, Discontinuities in the maximum-entropy inference, AIP Conference Proceedings 1553 (2013), 192-199. About • arXiv • Journal link We argue with the universality of the maximum-entropy inference that discontinuities of the maximum-entropy inference deserve further investigation. We explain an openness condition for the continuity of the inference. 1) I. Bengtsson, S. Weis, K. Życzkowski, Geometry of the set of mixed quantum states: An apophatic approach, in: Geometric Methods in Physics, P. Kielanowski, S. T. Ali, A. Odzijewicz, M. Schlichenmaier, T. Voronov (eds.), Basel: Birkhäuser, 2013, 175–197. About • arXiv • MPI MIS Preprint • Journal link State space models of a three-level quantum system are constructed by excluding characteristics that the state space does not have. Dimension dependent properties of finite-level quantum systems are revisited. Academic theses 3) S. Weis, Exponential families with incompatible statistics and their entropy distance, Doctoral Thesis, Erlangen, Germany, 2010. Electronic Library 2) S. Weis, Invariants for the ideal boundary of a tree, Diploma Thesis, Erlangen, Germany, 2004. PDF file (639kB) 1) S. Weis, Dynamics on graphs, Master Thesis, Bristol, UK, 2004. PDF file (955kB) Unpublished manuscripts • S. Weis, On a theorem by Kippenhahn. About • arXiv Kippenhahn proved that the numerical range is the convex hull of a real algebraic plane curve. We point out that higher-dimensional analogues are desirable for use in quantum mechanics and they are a challenge in real algebraic geometry. • presentations and travelling Events • The Fourteenth Workshop on Numerical Ranges and Numerical Radii, June 13th-18th, 2018, Munich, Germany • Entropy 2018: From Physics to Information Sciences and Geometry, May 14the-16th, 2018, Barcelona, Spain Selected conference talks 5) Classification of joint numerical ranges of three hermitian matrices of size three, The Fourteenth Workshop on Numerical Ranges and Numerical Radii, June 13th-18th, 2018, Munich, Germany, Slides (PDF, 6MB), Slides with less pictures (PDF, 1.8MB) 4) A new signature of quantum phase transitions from the numerical range, Entropy 2018: From Physics to Information Sciences and Geometry, May 14th - 16th, 2018, University of Barcelona, Spain, Slides (PDF, 268kB) 3) Stability of the set of quantum states, Workshop on "Probabilistic techniques and Quantum Information Theory", October 23rd - 27th, 2017, pertaining to the trimester "Analysis in Quantum Information Theory", Institut Henri Poincaré, Paris, France, Video (YouTube link) A similar talk was given at the colloquium of the Pure Mathematics Research Centre, November 17th, 2017, Queen's University Belfast, UK, Slides (PDF, 2.1MB) 2) On a theorem by Kippenhahn, Sums of Squares - Real Algebraic Geometry and its Applications, August 21st-25th, 2017, University of Innsbruck, Austria A similar talk was given at the Oberseminar über Algebra und Geometrie, November 9th, 2017, Technical University Dortmund, Germany, slides (PDF, 1.8MB) 1) A variation principle for ground spaces, Workskop on Operator Theory, Complex Analysis, and Applications, July 3rd-6th, 2017, Department of Mathematics of Instituto Superior Técnico, University of Lisbon, Portugal, Slides (PDF, 569 KB) Selected poster presentations 2) The rI-Closure of an Exponential Family and Ground Spaces, Conference "Quantum Information Theory", December 11th-15th, 2017, Institut Henri Poincaré, Paris, France, Poster (A0 size, PDF, 864kB) 1) Mysterious Discontinuity of Quantum Correlation, Joint IAS-ICTP School on Quantum Information Processing, January 18th-29th, 2016, Nanyang Executive Centre, Nanyang Technological University, Singapore, Poster (A2 size, PDF, 535kB) |
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