Stephan Weis
Mathematician


• 
profile

— 
I enjoy working on mathematical problems, mostly in geometry, matrix analysis, and functional analysis. Many of my past projects were inspired by problems of quantum information theory.

— 
I got my PhD in mathematics in 2009 from the University of ErlangenNuremberg, Germany,
where I wrote my thesis under the supervision of
Andreas Knauf and
Nihat Ay
in the mathematical physics group.
My thesis deals with the geometry of noncommutative exponential families (Gibbs states) with several parameters.
I completed five postdoctoral research programs:
– 
2010/2011, I worked on convex geometry at the University of ErlangenNuremberg.

– 
2011/2014, I studied the continuity of inference maps with a grant from
Arleta Szkoła,
in her project on quantum statistics at the
Max Planck Institute for Mathematics in the Sciences
in Leipzig, Germany.

– 
2015/2016 at the
University of Campinas, São Paulo, Brazil,
I began to study the algebraic geometry of joint numerical ranges (linear images of the convex set of density matrices),
which led to a
paper in the journal SIAGA in 2021.

– 
2016/2018, Jérémie Roland,
Atul S. Arora,
and I developed quantum algorithms for weak coin flipping at the Ecole Polytechnique de Bruxellles, Belgium
(results published in a
STOC paper
in 2019).

– 
201807/12, I resumed work on the algebraic geometry of joint numerical ranges at the
University of Coimbra, Portugal.

Thereafter, I completed a research project on the Choquet theory of energyconstrained density operators,
which is motivated by problems of quantum communication. I also completed a project on reduced density matrices.

— 
2020/2023, I taught in secondary schools (Gymnasium) in Berlin, Germany.

— 
In addition to mathematics, I am very much concerned about humancaused environmental damage, and climate change, in particular.
As an individual, whenever possible, I strive to minimize my carbon footprint.
I've collected a few links (in German) in the section "Weblinks zum Thema Klimawandel" below.

• 
research in mathematics

— 
publications: articles, theses
Preprints
2)
Weis, S.,
A note on faces of convex sets.
arXiv
1)
Arora, A. S.,
Roland, J.,
Vlachou, C., and Weis, S.,
Protocols for quantum weak coin flipping.
arXiv
Refereed journal papers
19) Weis, S. and
Gouveia, J.,
The face lattice of the set of reduced density matrices and its coatoms,
Information Geometry 6:1, 293326 (2023).
arXiv
•
Journal link
•
Fulltext
18) Plaumann, D.,
Sinn, R., and Weis, S.,
Kippenhahn's theorem for joint numerical ranges and quantum states,
SIAM Journal on Applied Algebra and Geometry 5:1, 86113 (2021).
arXiv
•
Journal link
17) Weis, S. and Shirokov, M. E.,
The face generated by a point, generalized affine constraints, and quantum theory,
Journal of Convex Analysis 28:3, 847870 (2021).
arXiv
•
Journal link
16) Weis, S. and Shirokov, M. E.,
Extreme points of the set of quantum states with bounded energy,
Russian Mathematical Surveys 76:1, 190192 (2021).
arXiv
•
Journal link
15) Weis, S.,
A variational principle for ground spaces,
Reports on Mathematical Physics 82:3, 317336 (2018).
arXiv
•
Journal link
14) Spitkovsky, I. M.
and Weis, S.,
Signatures of quantum phase transitions from the numerical range,
Journal of Mathematical Physics 59:12, 121901 (2018).
arXiv
•
Journal link
13) Szymański, K.,
Weis, S.,
and Życzkowski, K.,
Classification of joint numerical ranges of three hermitian matrices of size three,
Linear Algebra and its Applications 545, 148173 (2018).
arXiv
•
Journal link (open access)
12) Weis, S.,
Operator systems and convex sets with many normal cones,
Journal of Convex Analysis 25:1, 4164 (2018).
arXiv
•
Journal link
11) Spitkovsky, I. M.
and Weis, S.,
Preimages of extreme points of the numerical range, and applications,
Operators and Matrices 10:4, 10431058 (2016).
Special issue in memory of Leiba Rodman
arXiv
•
Journal link
10) Weis, S.,
Maximumentropy inference and inverse continuity of the numerical range,
Reports on Mathematical Physics 77:2, 251263 (2016).
arXiv
•
Journal link
9) Rodman, L.,
Spitkovsky, I. M.,
Szkoła, A.,
and Weis, S.,
Continuity of the maximumentropy inference: Convex geometry and numerical ranges approach,
Journal of Mathematical Physics 57:1, 015204 (2016).
Special issue: Operator Algebras and Quantum Information Theory
arXiv
•
Journal link
8) Weis, S.,
Knauf, A.,
Ay, N.,
and
Zhao, M.J.,
Maximizing the divergence from a hierarchical model of quantum states,
Open Systems & Information Dynamics 22:1, 1550006 (2015).
arXiv
•
SFI Working Paper
•
Journal link
7) Weis, S.,
Continuity of the maximumentropy inference,
Communications in Mathematical Physics 330:3, 12631292 (2014).
arXiv
•
MPI MIS Preprint
•
Journal link
6) Weis, S.,
Information topologies on noncommutative state spaces,
Journal of Convex Analysis 21:2, 339399 (2014).
arXiv
•
MPI MIS Preprint
•
Journal link
5) Weis, S.,
and Knauf, A.,
Entropy distance: New quantum phenomena,
Journal of Mathematical Physics 53:10, 102206 (2012).
arXiv
•
MPI MIS Preprint
•
Journal link
4) Weis, S.,
Duality of nonexposed faces,
Journal of Convex Analysis 19:3, 815835 (2012).
arXiv
•
MPI MIS Preprint
•
Journal link
3) Weis, S.,
A note on touching cones and faces,
Journal of Convex Analysis 19:2, 323353 (2012).
arXiv
•
Journal link
2) Weis, S.,
Quantum convex support,
Linear Algebra and its Applications 435:12, 31683188 (2011).
arXiv
•
Journal link (open access)
1) Voigt, I.
and Weis, S.,
Polyhedral Voronoi cells,
Contributions to Algebra and Geometry 51:2, 587598 (2010).
arXiv
•
Journal link (open access)
Refereed conference papers
5) Weis, S.,
Kippenhahn's construction revisited,
in: Ptak, M., et al. (eds.),
Operator and Matrix Theory, Function Spaces, and Applications,
IWOTA 2022,
Cham: Birkhäuser, 2024, 385396.
arXiv
•
Journal link
4)
Arora, A. S.,
Roland, J.,
and Weis, S.,
Quantum Weak Coin Flipping,
STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of
Computing, 2019, 205216.
arXiv
•
Final version (open access)
•
Journal link
3) Weis, S.,
The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics,
in: MohammadDjafari, A. and Barbaresco, F. (eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014),
AIP Conference Proceedings 1641, 173180 (2015).
arXiv
•
Journal link
2) Weis, S.,
Discontinuities in the maximumentropy inference,
in: von Toussaint, U. (ed.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2012),
AIP Conference Proceedings 1553, 192199 (2013).
arXiv
•
Journal link
1) Bengtsson, I.,
Weis, S.,
and Życzkowski, K.,
Geometry of the set of mixed quantum states: An apophatic approach,
in: Kielanowski, P., et al. (eds.) Geometric Methods in Physics,
Basel: Birkhäuser, 2013, 175197.
arXiv
•
MPI MIS Preprint
•
Journal link
Academic theses
3) Weis, S.,
Exponential families with incompatible statistics and their entropy distance,
Doctoral Thesis, Erlangen, Germany, 2010.
Electronic Library (open access)
2) Weis, S.,
Invariants for the ideal boundary of a tree,
Diploma Thesis, Erlangen, Germany, 2004.
PDF file (639kB)
1) Weis, S.,
Dynamics on graphs,
Master Thesis, Bristol, UK, 2004.
PDF file (955kB)
Unpublished manuscripts
3)
Arora, A. S.,
Roland, J.,
Vlachou, C., and Weis, S.,
Solutions to quantum weak coin flipping,
Cryptology ePrint Archive, paper 2022/1101, 2022.
2) Weis, S.,
Decomposition of symmetric separable states and ground state energy of bosonic systems.
arXiv
1) Weis, S.,
On a theorem by Kippenhahn.
arXiv

— 
presentations: slides, videos, posters
Slides and videos
6) Choquet's Theorem for Constrained Sets of Quantum States,
talk at the special session "Generalized Numerical Ranges, Operator Theory, and Quantum Information" at the 33rd
IWOTA, Krakow, Poland, September 2022,
slides (PDF, 564kB)
Video from a similar, longer talk at the MIAN online seminar "Quantum Probability, Statistics, Information", Steklov Mathematical Institute, Moscow, Russia, March 2021
5) Analysis of Generalized Gibbs States, talk at the conference
Entropy 2021: The Scientific Tool of the 21st Century,
Porto, Portugal,
May 2021,
slides (PDF, 1.1MB)
4) Quantum Weak Coin Flipping, talk at the
SUMA 2019  Reunión anual de la UMA junto a la SOMACHI,
Mendoza, Argentina,
September 2019,
slides (PDF, 147kB)
3) Classification of joint numerical ranges of three hermitian matrices of size three, talk at
The Fourteenth Workshop on Numerical Ranges and Numerical Radii,
Munich, Germany,
June 2018,
slides (PDF, 1.8MB)
2) A new signature of quantum phase transitions from the numerical range,
talk at the conference
Entropy 2018: From Physics to Information Sciences and Geometry,
University of Barcelona, Spain,
May 2018,
slides (PDF, 268kB)
1) Stability of the set of quantum states, talk at the Workshop "Probabilistic techniques and Quantum Information Theory" at the Trimester "Analysis in Quantum Information Theory", Institut Henri Poincaré, October 2017,
video
Slides (PDF, 2.1MB) from a similar talk at the Pure Mathematics Research Centre, Queens University Belfast, UK, November 2017
Posters
2) The rIClosure of an Exponential Family and Ground Spaces, poster presented at the Conference «Quantum Information Theory» at the Trimester «Analysis in Quantum Information Theory», Institut Henri Poincaré, December 2017,
poster (PDF, 863kB)
1) Mysterious Discontinuity of Quantum Correlation,
poster presented at the
Joint IASICTP School on Quantum Information Processing,
Nanyang Executive Centre,
Nanyang Technological University, Singapore,
January 2016,
poster (PDF, 535kB)

— 
web profiles
arXiv,
Google Scholar,
LinkedIn,
MathSciNet,
MGP,
ORCiD,
ResearchGate,
Scopus,
Web of Science,
XING,
zbMATH

— 
trivia: Erdős number = 3, Einstein number = 4

• 
Weblinks zum Thema Klimawandel (in German) 
— 
BLOG: KlimaLounge von Stefan Rahmstorf, Professor für Physik der Ozeane

— 
Volker Quaschning, Professor für Regenerative Energiesysteme

— 
ins Deutsche übersetzte
BlogArtikel von Skeptical Science

— 
Cranky Uncle, Spiel zur Stärkung der Abwehrkräfte gegen Falschinformationen (auch auf Deutsch und im Browser spielbar)

