相关论文: Kochen-Specker Vectors

A continuous map from R^m to R^N or from C^m to C^N is called k-regular if the images of any $k$ points are linearly independent. Given integers m and k a problem going back to Chebyshev and Borsuk is to determine the minimal value of N for…

Fix a prime power $q$ and parameters $1\leq t\leq k\leq n$, the corresponding Steiner system in the Grassmann scheme, or the $q$-Steiner system, is a collection $\mathfrak{B}$ of $k$-dimensional subspaces of $\mathbb{F}_{q}^n$ such that for…

We propose a kind of reverse Kochen-Specker theorem that amounts to generating orthomodular lattices (OMLs) with exactly one state that do not admit properties of the Hilbert space. We apply MMP algorithms to obtain smallest OMLs with 35…

For Hilbert spaces $\mathcal H\subseteq L^2(\mathbb R)$ we consider the convex sets $\mathcal D_+(\mathcal H)$ of Wigner-positive states (WPS), i.e.~density matrices over $\mathcal H$ with non-negative Wigner function. We investigate the…

We consider four (real or complex) dimensional hyper-K\"ahler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for…

The description of number of dual (quasy)-exactly solvable models with its hidden symmetry algebra has been given at different levels of analysis within the framework of generalized Kustaanheimo-Stiefel (KS)-transformations. It's shown that…

Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…

Bi-partite ribbon graphs arise in organising the large $N$ expansion of correlators in random matrix models and in the enumeration of observables in random tensor models. There is an algebra $\mathcal{K}(n)$, with basis given by bi-partite…

Stokes vectors and Discrete Wigner functions (DWF) provide two alternate ways of representing the polarization state of multiphoton systems. The Stokes vector associated with a n-photon polarization state is unique, and its Minkowski…

A {\it vector space partition} is here a collection $\mathcal P$ of subspaces of a finite vector space $V(n,q)$, of dimension $n$ over a finite field with $q$ elements, with the property that every non zero vector is contained in a unique…

It is shown that, given a reasonable continuity assumption regarding possessed values, it is possible to construct a Kochen-Specker obstruction for any coordinate and its conjugate momentum, demonstrating that at most one of these two…

A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett. 80, 1797 (1998)] is shown to be related with the smallest proof of the Kochen-Specker theorem currently known [Phys.…

This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental…

Recently Waegell and Aravind [J. Phys. A: Math. Theor. 45 (2012), 405301, 13 pages] have given a number of distinct sets of three-qubit observables, each furnishing a proof of the Kochen-Specker theorem. Here it is demonstrated that two of…

We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these…

It has recently been questioned whether the Kochen-Specker theorem is relevant to real experiments, which by necessity only have finite precision. We give an affirmative answer to this question by showing how to derive hidden-variable…

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…

We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp.…

For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use…