相关论文: Converting nonlocality into contextuality

Contextuality lays at the heart of quantum mechanics. In the prevailing opinion it is considered as a signature of 'quantumness' that classical theories lack. However, this assertion is only partially justified. Although contextuality is…

A hidden-variable model for quantum-mechanical spin, as represented by the Pauli spin operators, is proposed for systems illustrating the well-known no-hidden-variables arguments by Peres and Mermin (1990) and by Greenberger, Horne, and…

In 1993, Mermin (Rev. Mod. Phys. 65, 803--815) gave lucid and strikingly simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of dimensions four and eight by making use of what has since been referred to as the…

We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We…

For any state in four-dimensional system, the quantum violation of an inequality based on the Peres-Mermin proof for testing noncontextual realist models has experimentally been corroborated. In the Peres-Mermin proof, an array of nine…

Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting…

In contrast to the determinant, no algorithm is known for the exact determination of the permanent of a square matrix that runs in time polynomial in its dimension. Consequently, non interacting fermions are classically efficiently…

The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden variable theory. It is…

When computing the eigenstructure of matrix pencils associated with the passivity analysis of perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that the computed spectrum…

The Gauss-Manin connection of a family of hypersurfaces governs the change of the period matrix along the family. This connection can be complicated even when the equations defining the family look simple. When this is the case, it is…

Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…

We investigate small geometric configurations that furnish observable-based proofs of the Kochen-Specker theorem. Assuming that each context consists of the same number of observables and each observable is shared by two contexts, it is…

The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…

Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and…

We combine the coordinate method and Erlangen program in the framework of noncommutative geometry through an investigation of symmetries of noncommutative coordinate algebras. As the model we use the coherent states construction and the…

We introduce a constructive procedure that maps all spatial correlations of a broad class of states into temporal correlations between general quantum measurements. This allows us to present temporal phenomena analogous to genuinely…

To understand the solution of a linear, time-invariant differential-algebraic equation, one must analyze a matrix pencil (A,E) with singular E. Even when this pencil is stable (all its finite eigenvalues fall in the left-half plane), the…

The main ideas and some of the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional…

We present and experimentally demonstrate a novel non-classical phenomenon, bi-contextuality, observed in quantum systems prepared by two independent sources. This discovery plays a key role in the developing framework of network…