相关论文: Magic Three-Qubit Veldkamp Line and Veldkamp Space…

It is demonstrated that the magic three-qubit Veldkamp line occurs naturally within the Veldkamp space of combinatorial Grassmannian of type $G_2(7)$, $\mathcal{V}(G_2(7))$. The lines of the ambient symplectic polar space are those lines of…

The Veldkamp space, in the sense of Buekenhout and Cohen, of the generalized quadrangle GQ(4, 2) is shown not to be a (partial) linear space by simply giving several examples of Veldkamp lines (V-lines) having two or even three Veldkamp…

It is shown that the Veldkamp space of the unique generalized quadrangle GQ(2,4) is isomorphic to PG(5,2). Since the GQ(2,4) features only two kinds of geometric hyperplanes, namely point's perp-sets and GQ(2,2)s, the 63 points of PG(5,2)…

We introduce a point-line incidence geometry in which the commutation relations of the real Pauli group of multiple qubits are fully encoded. Its points are pairs of Pauli operators differing in sign and each line contains three pairwise…

Regarding a Dynkin diagram as a specific point-line incidence structure (where each line has just two points), one can associate with it a Veldkamp space. Focusing on extended Dynkin diagrams of type $\widetilde{D}_n$, $4 \leq n \leq 8$, it…

Given a remarkable representation of the generalized Pauli operators of two-qubits in terms of the points of the generalized quadrangle of order two, W(2), it is shown that specific subsets of these operators can also be associated with the…

We give a detailed description of the Veldkamp space of the smallest slim dense near hexagon. This space is isomorphic to PG(7, 2) and its 2^8 - 1 = 255 Veldkamp points (that is, geometric hyperplanes of the near hexagon) fall into five…

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…

We study the geometry of the space of Mermin pentagrams, objects that are used to rule out the existence of noncontextual hidden variable theories as alternatives to quantum theory. It is shown that this space of 12096 possible pentagrams…

For $N \geq 2$, an $N$-qubit doily is a doily living in the $N$-qubit symplectic polar space. These doilies are related to operator-based proofs of quantum contextuality. Following and extending the strategy of Saniga et al. (Mathematics 9…

The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal…

The geometry of the real four-qubit Pauli group, being embodied in the structure of the symplectic polar space W(7,2), is analyzed in terms of ovoids of a hyperbolic quadric of PG(7,2), the seven-dimensional projective space of order two.…

We introduce one of the most beautiful algebraic varieties known, a quintic hypersurface in projective five-space, which is invariant under the action of the Weyl group of $E_6$. This variety is intricately related with many other moduli…

We study certain physically-relevant subgeometries of binary symplectic polar spaces $W(2N-1,2)$ of small rank $N$, when the points of these spaces canonically encode $N$-qubit observables. Key characteristics of a subspace of such a space…

Disregarding the identity, the remaining 63 elements of the generalized three-qubit Pauli group are found to contain 12096 distinct copies of Mermin's magic pentagram. Remarkably, 12096 is also the number of automorphisms of the smallest…

We show that each connected component of the moduli space of smooth real binary quintics is isomorphic to an open subset of an arithmetic quotient of the real hyperbolic plane. Moreover, our main result says that the induced metric on this…

There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such…

We study theoretically analog multi-terminal Josephson junctions formed by gapped superfluids created upon resonant pumping of cavity exciton-polaritons. We study the $p$-like bands of a 5-terminal junction in the 4D parameter space created…

The varietal hypercube $VQ_n$ is a variant of the hypercube $Q_n$ and has better properties than $Q_n$ with the same number of edges and vertices. This paper shows that every edge of $VQ_n$ is contained in cycles of every length from 4 to…

The set of 63 real generalized Pauli matrices of three-qubits can be factored into two subsets of 35 symmetric and 28 antisymmetric elements. This splitting is shown to be completely embodied in the properties of the Fano plane; the…