Contextuality is an intriguing feature of quantum theory that excludes any noncontextual hidden variable theory of our nature. It is therefore a natural and important pursuit to detect as larger contextuality as possible. In the scenario to reveal contextuality through violation of noncontextuality inequality, the pursuit is to construct such inequality with large violations. In this paper, we present a simple method to extend arbitrary state-(in)dependent noncontextuality inequalities into ones with larger violations. By recursively applying the method, one can obtain noncontextuality inequalities with an arbitrary large violation. Moreover, the method also constructs quantum measurements and states to violate the new inequality.Contextuality is an intriguing feature of quantum theory that excludes any noncontextual hidden variable theory of our nature. It is therefore a natural and important pursuit to detect as larger contextuality as possible. In the scenario to reveal contextuality through violation of noncontextuality inequality, the pursuit is to construct such inequality with large violations. In this paper, we present a simple method to extend arbitrary state-(in)dependent noncontextuality inequalities into ones with larger violations. By recursively applying the method, one can obtain noncontextuality inequalities with an arbitrary large violation. Moreover, the method also constructs quantum measurements and states to violate the new inequality.

Physical Review AOct 26, 20210 citations

Some basic concepts of algebraic quantum theory

J. E. Roberts, Gert Roepstorff

Communications in Mathematical PhysicsDec 1, 196951 citations

Reformulating noncontextuality inequalities in an operational approach

Zhen‐Peng Xu, Debashis Saha, Hong-Yi Su +2 more

A new theory-independent noncontextuality inequality is presented [R. Kunjwal and R. W. Spekkens, Phys. Rev. Lett. 115, 110403 (2015)] based on a Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing noncontextuality inequalities, we show that such result can be generalized from a KS set to the noncontextuality inequalities not only for a state-independent scenario but also for a state-dependent scenario. The YO-13 ray and $n$ cycle ray are considered as examples.A new theory-independent noncontextuality inequality is presented [R. Kunjwal and R. W. Spekkens, Phys. Rev. Lett. 115, 110403 (2015)] based on a Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing noncontextuality inequalities, we show that such result can be generalized from a KS set to the noncontextuality inequalities not only for a state-independent scenario but also for a state-dependent scenario. The YO-13 ray and $n$ cycle ray are considered as examples.

arXiv:1509.06027Physical Review ADec 6, 201614 citations

Two concepts of noncontextuality in quantum mechanics

Gábor Hofer‐Szabó

arXiv:2203.01039Studies in History and Philosophy of Science Part AMar 8, 202213 citations

Dimension-dependent noncontextuality inequalities with large contexts

Xiang Zhan, Linxi Hu

Quantum theory shows a striking nonclassical feature of contextuality, which is also a crucial resource for quantum information processing. In this paper, we study the dependence of violating noncontextuality inequalities against the dimension of quantum systems. To this end, we consider the restrictions imposed on relations among measurements by limitation of dimensions. Based on the graph-theoretic approach to quantum contextuality, we construct noncontextuality inequalities using multiple mutually orthogonal projectors which are unique to high-dimensional quantum systems. We report two typical classes of dimension-dependent noncontextuality inequalities for one of which a violation implies the dimension of the quantum system is higher than a threshold, and for the other, different amounts of violations correspond to different thresholds of dimension. Our paper is expected to inspire more dimension-dependent noncontextuality inequalities.Quantum theory shows a striking nonclassical feature of contextuality, which is also a crucial resource for quantum information processing. In this paper, we study the dependence of violating noncontextuality inequalities against the dimension of quantum systems. To this end, we consider the restrictions imposed on relations among measurements by limitation of dimensions. Based on the graph-theoretic approach to quantum contextuality, we construct noncontextuality inequalities using multiple mutually orthogonal projectors which are unique to high-dimensional quantum systems. We report two typical classes of dimension-dependent noncontextuality inequalities for one of which a violation implies the dimension of the quantum system is higher than a threshold, and for the other, different amounts of violations correspond to different thresholds of dimension. Our paper is expected to inspire more dimension-dependent noncontextuality inequalities.

Physical Review ASep 10, 20215 citations

Reality and Measurement in Algebraic Quantum Theory

Masanao Ozawa, Jeremy Butterfield, Hans Halvorson +3 more

arXiv:1606.00108Springer proceedings in mathematics & statisticsJan 1, 201812 citations

n

cycle ray are considered as examples.