## Stephan WeisPostdoctoral ScholarContactCentre for Quantum Information and Communication Ecole Polytechnique de Bruxelles Université Libre de Bruxelles 50 av. F.D. Roosevelt - CP165/59 B-1050 Bruxelles Belgium phone: +32-2-650 29 72 e-mail: maths@stephan-weis.info |
• research in mathematics and quantum informationstate spaces of operator systems joint numerical range maximum-entropy states quantum correlations geometry of ground states weak coin flipping • profiles on internet databases
• arXiv • Google Scholar • ResearchGate • ResearcherID (Web of Science™) • ORCID • currículo lattes (CNPq) (in Portuguese) • publications
Preprints• S. Weis (submitted) Operator systems and convex sets with many normal conesarXiv • K. Szymański, S. Weis, K. Życzkowski (submitted) Classification of joint numerical ranges of three hermitian matrices of size threearXiv • I. M. Spitkovsky, S. Weis (in press) Pre-images of extreme points of the numerical range, and applications,Operators and Matrices arXiv Articles in research journals10) S. Weis (2016) Maximum-entropy inference and inverse continuity of the numerical range,Reports on Mathematical Physics 77(2) 251-263 About • arXiv • Journal link 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 (2016) Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach,Journal of Mathematical Physics 57(1) 015204 About • arXiv • Journal link We dwell on convex geometry to study maximum-entropy states and quantum correlations. We explore unique pre-images of numerical range points to address the case of two quantum observables. 8) S. Weis, A. Knauf, N. Ay, M.-J. Zhao (2015) Maximizing the divergence from a hierarchical model of quantum states,Open Systems & Information Dynamics 22(1) 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 (2014) Continuity of the maximum-entropy inference,Communications in Mathematical Physics 330(3) 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 (2014) Information topologies on non-commutative state spaces,Journal of Convex Analysis 21(2) 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 (2012) Entropy distance: New quantum phenomena,Journal of Mathematical Physics 53(10) 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 (2012) Duality of non-exposed faces,Journal of Convex Analysis 19(3) 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 (2012) A note on touching cones and faces,Journal of Convex Analysis 19(2) 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 (2011) Quantum convex support,Linear Algebra and its Applications 435(12) 3168-3188 About • arXiv • Journal link 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.
2a) S. Weis (2012)
Correction, ibid. 436(1) xviAbout • Journal link Spectral values have to be used in place of eigenvalues. The arXiv-version has this error removed, see also Remark 6 in S. Weis, A. Knauf (2012) Entropy distance: New quantum phenomena,
JMP 53(10) 102206
1) I. Voigt, S. Weis (2010) Polyhedral Voronoi cells,Contributions to Algebra and Geometry 51(2) 587-598 About • arXiv • Journal link 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. Articles in conference proceedings3) S. Weis (2015) The MaxEnt extension of a quantum Gibbs family, convex geometry
and geodesics,
34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering,
Château du Clos Lucé, Amboise, France, 21-26 September 2014,
eds. A. Mohammad-Djafari, F. Barbaresco,
AIP Conference Proceedings 1641 173-180About • 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 (2013) Discontinuities in the maximum-entropy inference,
32nd International Workshop on Bayesian Inference and Maximum Entropy Methods
in Science and Engineering, Garching, Germany, 15-20 July 2012, ed. U. von Toussaint,
AIP Conference Proceedings 1553 192-199About • 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 (2013) Geometry of the set of mixed quantum states: An apophatic approach,
Geometric Methods in Physics, XXX Workshop, Białowieża, Poland,
June 26 to July 2, 2011, eds. P. Kielanowski, S. T. Ali, A. Odzijewicz, M. Schlichenmaier,
T. Voronov, Springer Basel, Trends in Mathematics 175-197About • 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 theses3) S. Weis (2010) Exponential families with incompatible statistics and their entropy distance,
Doctoral Thesis, University of Erlangen, GermanyElectronic Library 2) S. Weis (2004) Invariants for the ideal boundary of a tree,
Diploma Thesis, University of ErlangenPDF file (639kB) 1) S. Weis (2004) Dynamics on graphs,
Master Thesis, University of Bristol, Bristol, UKPDF file (955kB) • presentations and travelling
Upcoming events
• Information Topologies on Non-Commutative State Spaces,
The 11th Conference on the Theory of
Quantum Computation, Communication and Cryptography,
September 27–29, 2016, Berlin, Germany,
Poster (PDF, 745 kB)
Slides from talks
• Continuity of many-party correlations,
Invited Minisymposium Linear Algebra and Quantum Computation,
20th Conference of the International Linear Algebra Society,
July 11-15, 2016, KU Leuven, Leuven, Belgium,
Slides (PDF, 578kB)
• Algebraic Geometry of the Joint Numerical Range,
IV Jornada da Informação,
March 28-29, 2016,
Unicamp, Limeira, Brazil,
Slides (PDF, 5.6 MB)
• A classification of the joint numerical range of three hermitian 3-by-3 matrices,
Workshop on Positive Semidefinite Rank, Program
Semidefinite and Matrix Methods for Optimization and Communication,
February 1-21, 2016,
Institute for Mathematical Sciences,
National University of Singapore, Singapore,
Slides (PDF, 1.1 MB)
• Quantum correlations and convex hulls of plane affine curves,
Seminar of the research group
GAUGE THEORY AND ALGEBRAIC GEOMETRY,
September 24, 2015, Departamento de Matemática, IMECC Unicamp, Campinas,
Brazil, Slides of PART I (PDF, 385 kB)
Posters
• Mysterious Discontinuity of Quantum Correlation,
Joint IAS-ICTP School on Quantum Information Processing,
January 18-29, 2016,
Nanyang Executive Centre,
Nanyang Technological University, Singapore,
Poster (A2 size, PDF, 535kB)
• Computing many-party quantum correlations — analytical results, Conference
Theory of Quantum Computation, Communication and Cryptography,
May 20–22, 2015, Brussels, Belgium,
Poster (A0 size, PDF, 2.1MB)
• Continuity in Gibbsian inference, Workshop
Operator structures in quantum information theory, February 26-March 2, 2012, Banff, Canada, Poster (A0 size, PDF, 971kB)
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