• Corpus ID: 197485279

Rank of contextuality

  title={Rank of contextuality},
  author={Karol Horodecki and Jing-nan Zhou and Maciej Stankiewicz and Roberto Salazar and Paweł Horodecki and Robert Raussendorf and Ryszard Horodecki and Ravishankar Ramanathan and E. Tyhurst},
  journal={Bulletin of the American Physical Society},
(Dated: Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantifier of this resource, the rank of contextuality (RC). We define RC as the minimum number of non-contextual behaviors that are needed to simulate a contextual behavior. We show that the logarithm of RC is a natural contextuality measure satisfying several properties considered in the spirit of the resource-theoretic approach. The properties include… 

Figures from this paper


Noncontextual Wirings.
This work introduces noncontextual wirings: a class of contextuality-free operations with a clear operational interpretation and a friendly parametrization that complete a unified resource-theoretic framework for contextuality and Bell nonlocality.
Quantifying contextuality.
This work provides a universal framework for quantifying contextuality, and gives analytical formulas for the proposed measures for some contextual systems, showing in particular that the Peres-Mermin game is by order of magnitude more contextual than that of Klyachko et al.
A Combinatorial Approach to Nonlocality and Contextuality
AbstractSo far, most of the literature on (quantum) contextuality and the Kochen–Specker theorem seems either to concern particular examples of contextuality, or be considered as quantum logic. Here,
State independent contextuality advances one-way communication
This article presents a family of distributed computing tasks pertaining to every logical proof of Kochen–Specker contextuality in two different one-way communication scenarios and shows that quantum communication comprised of every KS set of vectors outperforms classical communication and perfectly accomplish the task in both the aforementioned scenarios.
Resource theory of contextuality
  • B. Amaral
  • Philosophy
    Philosophical Transactions of the Royal Society A
  • 2019
In this contribution, recent developments towards a resource theory of contextuality and connections with operational applications of this property are reviewed.
The sheaf-theoretic structure of non-locality and contextuality
It is shown that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections, and a linear algebraic approach to computing these obstructions is described, which allows a systematic treatment of arguments for non- Locality and contextuality.
Axiomatic approach to contextuality and nonlocality
A unified axiomatic approach to contextuality and non-locality based on the fact that both are resource theories, which makes use of the known distillation protocol of bipartite nonlocality to show how contextual resources can be distilled.
Logic of Local Inference for Contextuality in Quantum Physics and Beyond
This work forms a logic of local inference by using context-sensitive theories and models in regular categories that provides a uniform framework for local consistency, and lays a foundation for high-level methods of detecting, proving, and moreover using contextuality as computational resource.
Contextuality supplies the ‘magic’ for quantum computation
This work proves a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer.
Contextuality as a Resource for Models of Quantum Computation with Qubits.
This work establishes contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits for measurement-based quantum computation.