Related papers: SICs, the Stabilizer Polytope and Majorization
This paper presents the theory of Bohr-Sommerfeld-Heisenberg quantization of a completely integrable Hamiltonian system in the context of geometric quantization. The theory is illustrated with several examples.
The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all…
In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is…
We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~$\{0,1\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\Stab{V}{\Part}$ of~$V$. We…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
Molecular packing, crystallinity, and texture of semiconducting polymers are often critical to performance. Although frame-works exist to quantify the ordering, interpretations are often just qualitative, resulting in imprecise and liberal…
We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense…
We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which…
This paper deals with transportation polytopes in the probability simplex (that is, sets of categorical bivariate probability distributions with prescribed marginals). Information projections between such polytopes are studied, and a…
We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of…
Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…
A general symmetric-informationally-complete (GSIC)-positive-operator-valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC POVMs with a fixed average purity. In this paper we provide a general…
We explore the conjectured duality between a class of large $N$ matrix integrals, known as multicritical matrix integrals (MMI), and the series $(2m-1,2)$ of non-unitary minimal models on a fluctuating background. We match the critical…
Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in…
We study a generalization of specialized Simpson's main estimate in the context of cyclic harmonic $G$-bundles induced by split automorphisms. We apply it to the classification of Toda type $G$-harmonic bundles.
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via…