Related papers: Mermin pentagrams arising from Veldkamp lines for …
The possible spectra of one-particle reduced density matrices that are compatible with a pure multipartite quantum system of finite dimension form a convex polytope. We introduce a new construction of inner- and outer-bounding polytopes…
This is the first of a series of papers considering symmetry properties of quantum systems over 2D graphs or manifolds, with continuous spins, in the spirit of the Mermin--Wagner theorem. In the model considered here (quantum rotators) the…
We perform a global analysis of the space of consistent 6D quantum gravity theories with N = 1 supersymmetry, including models with multiple tensor multiplets. We prove that for theories with fewer than T = 9 tensor multiplets, a finite…
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with…
The attempted classification of regular algebras of global dimension four, so-called quantum $\mathbb P^3$s, has been a driving force for modern research in noncommutative algebra. Inspired by the work of Artin, Tate, and Van den Bergh,…
Mermin inequalities are derived for systems of three-state particles (qutrits) employing three local measurement settings. These establish perfect correlations which violate local realistic bounds more strongly than those previously…
An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set…
Following the spirit of a recent work of one of the authors (J. Phys. A: Math. Theor. 44 (2011) 045301), the essential structure of the generalized Pauli group of a qubit-qu$d$it, where $d = 2^{k}$ and an integer $k \geq 2$, is recast in…
We present two new families of Wilson loop operators in N= 6 supersymmetric Chern-Simons theory. The first one is defined for an arbitrary contour on the three dimensional space and it resembles the Zarembo's construction in N=4 SYM. The…
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…
Using a standard technique sometimes (inaccurately) known as Burnside's Lemma, it is shown that the Veldkamp space of the near hexagon L_3 times GQ(2, 2) features 156 different types of lines. We also give an explicit description of each…
A new tropical plactic algebra is introduced in which the Knuth relations are inferred from the underlying semiring arithmetics, encapsulating the ubiquitous plactic monoid $\mathcal{P}_n$. This algebra manifests a natural framework for…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements:…
The purpose of this note is to report, in narrative rather than rigorous style, about the nice geometry of $6$-division points on the Fermat cubic $F$ and various conics naturally attached to them. Most facts presented here were derived by…
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally…
Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and…
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a…
We study six-dimensional N=(1,0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups -…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…