40 citations · 250 across the 28 of their papers we have counts for
32 papers
Extreme points and faces in the moment problem
Didier Henrion, Martin Kružík, Stephan Weis
The polyconvex envelope, used in the calculus of variations and elasticity theory, was expressed by Dacorogna pointwise as a linear program on finitely atomic measures on the space…
Polyconvexity with Moments and Sums of Squares
Giovanni Fantuzzi, Didier Henrion, Martin Kru{ž}ík +2
A function of a matrix is polyconvex when it can be expressed as a convex function of the matrix minors. Polyconvexity is a regularity condition ensuring existence of minimizers in…
The joint numerical range of three hermitian matrices
Piotr Pikul, Ilya Spitkovsky, Konrad Szymański +2
We analyze the joint numerical range of three hermitian matrices of order four. In the generic case, this three-dimensional convex set has a smooth boundary. We analyze non-gen…
Matrix systems, algebras, and open maps
Stephan Weis
Every state on the algebra of complex nxn matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that…
A note on faces of convex sets
Stephan Weis
The faces of a convex set owe their relevance to an interplay between convexity and topology that is systematically studied in the work of Rockafellar. Infinite-dimensional convex…
Protocols for Quantum Weak Coin Flipping
Atul Singh Arora, Jérémie Roland, Chrysoula Vlachou +1
Weak coin flipping is an important cryptographic primitive$\unicode{x2013}$it is the strongest known secure two-party computation primitive that classically becomes secure only und…
Kippenhahn's construction revisited
Stephan Weis
Kippenhahn discovered that the numerical range of a complex square matrix is the convex hull of a plane real algebraic curve. Here, we present an example of a convex set, which has…
Quantum marginals, faces, and coatoms
Stephan Weis, João Gouveia
Many problems of quantum information theory rely on the set of quantum marginals. A precise knowledge of the faces of this convex set is necessary, for example, in the reconstructi…
Decomposition of symmetric separable states and ground state energy of bosonic systems
Stephan Weis
We prove that every symmetric separable state admits a convex decomposition into symmetric pure product states. While the result is not new in itself, here we focus on convex geome…
The face generated by a point, generalized affine constraints, and quantum theory
Stephan Weis, Maksim Shirokov
We analyze faces generated by points in an arbitrary convex set and their relative algebraic interiors, which are nonempty as we shall prove. We show that by intersecting a convex…
Extreme points of the set of quantum states with bounded energy
Stephan Weis, Maksim Shirokov
We show that for any energy observable every extreme point of the set of quantum states with bounded energy is a pure state. This allows us to write every state with bounded energy…
Kippenhahn's Theorem for joint numerical ranges and quantum states
Daniel Plaumann, Rainer Sinn, Stephan Weis
Kippenhahn's Theorem asserts that the numerical range of a matrix is the convex hull of a certain algebraic curve. Here, we show that the joint numerical range of finitely many Her…
Quantum Weak Coin Flipping
Atul Singh Arora, Jérémie Roland, Stephan Weis
We investigate weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating player can try to…
On a theorem by Kippenhahn
Stephan Weis
Kippenhahn discovered a real algebraic plane curve whose convex hull is the numerical range of a matrix. The correctness of this theorem was called into question when Chien and Nak…
A variation principle for ground spaces
Stephan Weis
The ground spaces of a vector space of hermitian matrices, partially ordered by inclusion, form a lattice constructible from top to bottom in terms of intersections of maximal grou…
A new signature of quantum phase transitions from the numerical range
Ilya M. Spitkovsky, Stephan Weis
The ground state energy of a finite-dimensional one-parameter Hamiltonian and the continuity of a maximum-entropy inference map are discussed in the context of quantum critical phe…
Operator systems and convex sets with many normal cones
Stephan Weis
The state space of an operator system of -by- matrices has, in a sense, many normal cones. Merely this convex geometrical property implies smoothness qualities and a clusteri…
Classification of joint numerical ranges of three hermitian matrices of size three
Konrad Szymański, Stephan Weis, Karol Życzkowski
The joint numerical range of three hermitian -by- matrices is a convex and compact subset in . Generically we find that is a thr…
Pre-images of extreme points of the numerical range, and applications
Ilya M. Spitkovsky, Stephan Weis
We extend the pre-image representation of exposed points of the numerical range of a matrix to all extreme points. With that we characterize extreme points which are multiply gener…
Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach
Leiba Rodman, Ilya M. Spitkovsky, Arleta Szkoła +1
We study the continuity of an abstract generalization of the maximum-entropy inference - a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body w…
Maximum-entropy inference and inverse continuity of the numerical range
Stephan Weis
We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the se…
The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics
Stephan Weis
We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inferen…
Maximizing the divergence from a hierarchical model of quantum states
Stephan Weis, Andreas Knauf, Nihat Ay +1
We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from…
Discontinuities in the Maximum-Entropy Inference
Stephan Weis
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fi…