SAMOP 2021 – scientific programme
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QI: Fachverband Quanteninformation
QI 13: Quantum Information and Foundations II
QI 13.5: Talk
Friday, September 24, 2021, 11:45–12:00, H4
On Quantum Sets of Non-Contextuality Inequalities — •Lina Vandré1 and Marcelo Terra Cunha2 — 1Universität Siegen, Germany — 2Universidade Estadualde Campinas, Brazil
Bell inequalities and other non-contextuality (NC) inequalities are fundamental for quantum information processing. The underlying scenarios can be represented by exclusivity graphs [1]. While a Bell or NC scenario has a unique graph, the same graph can correspond to different scenarios. Originally there is no distinction between parties. In Ref. [2], the approach got modified by using coloured graphs to represent scenarios of multiple parties. In general, coloured graphs describes the underlying Bell or NC scenarios more precisely. The mathematical properties of the graph are then used for finding the classical and the quantum bound of the inequality. Also the complete set of behaviours allowed by classical probability theory as well as the quantum set can be characterised using these methods.
In this contribution I will discuss the coloured graph approach to the CHSH inequality and provide a method to characterise the corresponding quantum set. Moreover, I introduce a family of subgraphs of the CHSH graph which have the same underlying non-coloured graph (shadow) as the CHSH graph but represent different Bell or NC scenarios. I will compare the quantum sets of different graphs from this family and show how changes in the graph influence the underlying scenario and the quantum set [3].
[1] Phys. Rev. Lett. 112, 040401 (2014) [2] J. Phys. A: Math. Theor. 47, 4240214 (2014) [3] arXiv:2105.08561