Related papers: Contextuality in phase space
Contextuality, the impossibility of assigning a single random variable to represent the outcomes of the same measurement procedure under different experimental conditions, is a central aspect of quantum mechanics. Thus defined, it appears…
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an…
The geometry of cosets in the subgroups H of the two-generator free group G =\textless{} a, b \textgreater{} nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. Dessins stabilize…
A set of quantum measurements exhibits quantum contextuality when any consistent value assignment to the measurement outcomes leads to a contradiction with quantum theory. In the original Kochen-Specker-type of argument the measurement…
Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here…
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…
When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that…
We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary…
We investigate the violation of non-contextuality by a class of continuous variable states, including variations of entangled coherent states (ECS's) and a two-mode continuous superposition of coherent states. We generalise the…
The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different…
In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose…
Contextuality means non-existence of a joint distribution for random variables recorded under mutually incompatible conditions, subject to certain constraints imposed on how the identity of these variables may change across these…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
The Wigner-Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…
A generalisation of quantum contextuality to the case of many indentical particles is presented. The model consists of a finite collection of modes that can be occupied by N particles, either bosons or fermions. Measurement scenarios allow…
Quantum contextuality refers to the impossibility of assigning a predefined, intrinsic value to a physical property of a system independently of the context in which the property is measured. It is, perhaps, the most fundamental feature of…
This paper provides a framework for characterizing sequential scenarios, allowing for the identification of contextuality given empirical data, and then provides precise operational interpretations in terms of the possible hidden variable…
Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To…
Matrix pencils provide a robust method for finding simultaneous eigensystems of mutually commuting degenerate operators. In this paper, we utilize these techniques to investigate the quantum logical structures of the Peres-Mermin square and…