Related papers: SICs, the Stabilizer Polytope and Majorization
In this paper we develop three different subjects. We study and prove alternative versions of Hrushovski's "Stabilizer Theorem", we generalize part of the basic theory of definably amenable NIP groups to NTP2 theories, and finally, we use…
In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually…
We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the…
It is well-known in classical frame theory that overcomplete representations of a given vector space provide robustness to additive noise on the frame coefficients of an unknown vector. We describe how the same robustness can be shown to…
We give a combinatorial characterization of the identities holding in the semiring of all upper triangular Boolean $n\times n$-matrices and apply the characterization to computational complexity of identity checking, finite axiomatizability…
Polarization singularities including bound states in the continuum (BICs) and circularly polarized states have provided promising opportunities in the manipulation of light waves. Previous studies show that BICs in photonic crystal slabs…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite…
Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions. Factorizations of spinor polynomial corresponds to the…
An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c=m/2, where m is an integer. The models are diagonalized by automatically…
Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations…
In this paper we consider local centralizer classification and rigidity of some toral automorphisms. In low dimensions we classify up to finite index possible centralizers for volume preserving diffeomorphisms $f$ $C^{1}-$close to an…
We describe and classify countable Boolean rings (which may or may not have a multiplicative identity) with finitely many distinguished ideals whose elementary theory is countably categorical. This extends the description by Macintyre and…
We identify the obstructions for the functoriality and the uniqueness of the totalization functor, (partially) defined on the category of simplicial objects in the homotopy category of a stable model category, and we use a result from the…
Statistical ensemble formalism of Kim, Mandel and Wolf (J. Opt. Soc. Am. A 4, 433 (1987)) offers a realistic model for characterizing the effect of stochastic non-image forming optical media on the state of polarization of transmittedlight.…
We study modular ortholattices in the variety generated by the finite dimensional ones from an equational and geometric point of view. We relate this to coordinatization results.
Studying and understanding social networks is crucial for accurately defining ideological polarization, since they enable precise modeling of social structures. One of the limitations of many methods for quantifying polarization on networks…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…