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Simplest Kochen-Specker Set.

Adán Cabello1

  • 1Universidad de Sevilla, Universidad de Sevilla, Departamento de Física Aplicada II, E-41012 Sevilla, Spain and Instituto Carlos I de Física Teórica y Computacional, E-41012 Sevilla, Spain.

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|November 21, 2025
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Summary
This summary is machine-generated.

Researchers discovered a more symmetrical Kochen-Specker (KS) set in quantum physics. This new set uses fewer bases (14) and refutes a previous conjecture, advancing our understanding of quantum correlations and strategies.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics

Background:

  • Kochen-Specker (KS) sets are crucial for understanding quantum correlations and nonlocal games.
  • Previous minimal KS sets in three-level systems were asymmetrical and required many bases.

Purpose of the Study:

  • To present a novel, more symmetrical Kochen-Specker set.
  • To establish a new record for the minimum number of bases required for such sets.
  • To refute a specific conjecture regarding bipartite quantum strategies.

Main Methods:

  • Construction of a new Kochen-Specker set in three-level systems.
  • Analysis of the symmetry and number of bases required.
  • Demonstration of its application in nonlocal games and quantum strategies.

Main Results:

  • A new, highly symmetrical Kochen-Specker set is presented.
  • This set achieves a new record minimum of 14 bases.
  • The set refutes Conjecture 2 from Cabello's work on bipartite quantum strategies.
  • It establishes a new record for qutrit-qutrit perfect strategies with 5-9 inputs.

Conclusions:

  • The discovered KS set is simpler and more fundamental than previous examples.
  • This work advances the study of quantum correlations and nonlocal games.
  • It provides a new benchmark for quantum strategy complexity.