Related papers: Kochen-Specker Vectors
It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10^9 critical parity proofs of the Kochen-Specker theorem. The geometrical properties of the rays are described, an overview of…
The concept of \emph{almost orthogonal vectors}, i.e.\ vectors whose cosine similarity is close to $0$, relates to topics both in pure mathematics and in coding theory under the guises of spherical packing and spherical codes. In recent…
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other…
We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product…
We present a method to obtain sets of vectors proving the Bell-Kochen-Specker theorem in dimension $n$ from a similar set in dimension $d$ ($3\leq d<n\leq 2d$). As an application of the method we find the smallest proofs known in dimension…
Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present…
Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of…
This paper takes a step towards theoretical analysis of the relationship between word embeddings and context embeddings in models such as word2vec. We start from basic probabilistic assumptions on the nature of word vectors, context…
Several arguments demonstrate the incompatibility between Quantum Mechanics and classical Physics. Bell's inequalities and Greenberger-Horne-Zeilinger (GHZ) arguments apply to specific non-classical states. The Kochen-Specker (KS) one,…
Zeckendorf's Theorem says that for all $k \geq 3$, every nonnegative integer has a unique $k$-Zeckendorf representation as a sum of distinct $k$-bonacci numbers, where no $k$ consecutive $k$-bonacci numbers are present in the…
A mixed Steiner system MS$(t,k,Q)$ is a set (code) $C$ of words of weight $k$ over an alphabet $Q$, where not all coordinates of a word have the same alphabet size, each word of weight $t$, over $Q$, has distance $k-t$ from exactly one…
The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics in such a way that the algebraic relations among the values of dynamical variables whose self-adjoint operators…
The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…
In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on noncommutative algebras. Accordingly, contextuality (as an impossibility of assigning binary values to projection operators independently of their…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
Quantum contextuality takes an important place amongst the concepts of quantum computing that bring an advantage over its classical counterpart. For a large class of contextuality proofs, aka. observable-based proofs of the Kochen-Specker…
We construct the vertex operator representation for the Affine Kac-Moody $SL(M+K+1)$ algebra, which is relevant for the construction of the soliton solutions of the constrained KP hierarchies. The oscillators involved in the vertex operator…
A pure quantum state of $n$ parties associated with the Hilbert space $\CC^{d_1}\otimes \CC^{d_2}\otimes\cdots\otimes \CC^{d_n}$ is called $k$-uniform if all the reductions to $k$-parties are maximally mixed. The $n$ partite system is…
We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…
This article presents a simple characterization for entangled vectors in a finite dimensional Hilbert space $H$. The characterization is in terms of the coefficients of an expansion of the vector relative to an orthonormal basis for $H$.…