Related papers: Quantum Contextual Hypergraphs, Operators, Inequal…
Although `quantum contextuality' is one of the most fundamental non-classical feature, its generic role in information processing and computation is an open quest. In this article, we present a family of distributed computing tasks…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
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 key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, understood as a resource for quantum computation, it…
A fundamental problem in quantum computation and quantum information is finding the minimum quantum dimension needed for a task. For tasks involving state preparation and measurements, this problem can be addressed using only the…
We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multi-photon sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such general…
We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an…
It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)], that the Kochen-Specker theorem applies to two dimensions if one uses Positive Operator-Valued Measures. We show that contextuality in their models…
This paper presents the quantum Moebius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Moebius strip and Penrose's `impossible objects'. The hypergraph is constructed using faithful orthogonal…
Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some…
The Kochen-Specker (KS) theorem is a corner-stone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed…
As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks.…
The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and…
The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum…
We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong…
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with…
Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…
A Kochen-Specker (KS) set is a specific set of projectors and measurement contexts that prove the Bell-Kochen-Specker contextuality theorem. The simplest known KS sets in Hilbert space dimensions $d=3,4,5,6,8$ are reproduced, and several…
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…
Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the…