Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions

Pavičić, Mladen (2025) Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions. Entropy, 27 (1). ISSN 1099-4300

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Abstract

Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen–Specker and non-Kochen–Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field.

Item Type:	Article
Uncontrolled Keywords:	quantum contextuality; hypergraph contextuality; MMP hypergraphs; operator contextuality; random generation; Kochen–Specker sets; non-Kochen–Specker contextual sets
Subjects:	NATURAL SCIENCES > Physics > General and Classical Physics
Divisions:	Center of Excellence for Advanced Materials and Sensing Devices
Projects:	Project title Project leader Project code Project type Potpora vrhunskim istraživanjima Centra izvrsnosti za napredne materijale i senzore- Mile Ivanda; Milko Jakšić; Mario Stipčević; Marko Kralj KK.01.1.1.01.0001 EK
Depositing User:	Ana Zečević
Date Deposited:	29 Apr 2025 09:00
URI:	http://fulir.irb.hr/id/eprint/9775
DOI:	10.3390/e27010054

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