Quantum theory allows for absolute maximal contextuality

Abstract

Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality witnesses can be expressed as a sum $S$ of $n$ probabilities, and the independence number $\alpha$ and the Tsirelson-like number $\vartheta$ of the corresponding exclusivity graph are, respectively, the maximum of $S$ for noncontextual theories and for the theory under consideration. A theory allows for absolute maximal contextuality if it has scenarios in which $\vartheta /\alpha$ approaches $n$. Here we show that quantum theory allows for absolute maximal contextuality despite what is suggested by the examination of the quantum violations of Bell and noncontextuality inequalities considered in the past. Our proof is not constructive and does not single out explicit scenarios. Nevertheless, we identify scenarios in which quantum theory allows for almost absolute maximal contextuality.

REVTeX4, 6 pages, 1 figure

References in corpus (11)

• Simple explanation of the quantum violation of a fundamental inequality
• Unbounded violation of tripartite Bell inequalities
• Wigner function negativity and contextuality in quantum computation on rebits
• (Non-)Contextuality of Physical Theories as an Axiom
• Necessary and sufficient condition for quantum state-independent contextuality
• Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
• Measurement sharpness cuts nonlocality and contextuality in every physical theory
• Simple explanation of the quantum limits of genuine $n$-body nonlocality
• Multigraph approach to quantum non-locality
• Exclusivity principle and the quantum bound of the Bell inequality
• The Exclusivity Principle and the Set of Quantum Correlations

Cited by in corpus (14)

• Kochen-Specker Contextuality
• Simple method for experimentally testing any form of quantum contextuality
• Measures of Contextuality and Noncontextuality
• Contextuality and Noncontextuality Measures and Generalized Bell Inequalities for Cyclic Systems
• Experimental test of contextuality in quantum and classical systems
• Non-deterministic semantics for quantum states
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
• Contextuality and bundle diagrams
• Experimental demonstration of the connection between quantum contextuality and graph theory
• Experimental test of high-dimensional quantum contextuality based on contextuality concentration
• Large violations in Kochen Specker contextuality and their applications
• Bosonic Indistinguishability-Dependent Contextuality
• Twenty years of quantum contextuality at USTC
• Graph-theoretic approach to dimension witnessing