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Non-Classical Correlations in n-Cycle Setting.

Kishor Bharti1, Maharshi Ray1, Leong-Chuan Kwek1,2,3

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Summary
This summary is machine-generated.

This study explores quantum resources like Kochen-Specker-Klyachko (KS) boxes and Popescu-Rohlrich (PR) boxes in n-cycle settings. It provides criteria for simulating KS boxes and analyzes conditions for quantum violations in non-contextuality inequalities.

Keywords:
KS BoxNon-contextuality inequalityPR Box

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Area of Science:

  • Quantum Information Theory
  • Quantum Computation
  • Quantum Communication

Background:

  • Entanglement and Bell non-locality are key for quantum communication.
  • Contextuality, a generalization of Bell non-locality, is crucial for quantum computation.
  • The practical and fundamental aspects of these non-classical resources require further understanding.

Purpose of the Study:

  • To explore non-classical correlations in quantum and super-quantum resources within the n-cycle setting.
  • To analyze Kochen-Specker-Klyachko (KS) boxes, n-cycle non-contextuality inequalities, and Popescu-Rohlrich (PR) boxes.
  • To establish criteria for classical simulation of KS boxes and conditions for quantum violations of n-cycle inequalities.

Main Methods:

  • Analysis of correlations in n-cycle settings involving KS boxes and PR boxes.
  • Development of criteria for optimal classical simulation of arbitrary n-dimensional KS boxes.
  • Investigation of n-cycle non-contextuality inequalities for odd and even cycles, including phase space extension.
  • Simulation of generalized PR boxes using KS boxes.

Main Results:

  • Criteria for optimal classical simulation of arbitrary n-dimensional KS boxes are provided.
  • Conditions for quantum violation of n-cycle non-contextuality inequalities for both odd and even cycles are discussed.
  • A simple extension of even cycle non-contextuality inequalities to the phase space case is presented.
  • A generalized PR box is simulated using a KS box, yielding novel insights.

Conclusions:

  • The study connects generalized PR boxes, arbitrary dimensional KS boxes, and n-cycle non-contextuality inequalities.
  • It offers a pathway for studying these contextual and nonlocal resources at their intersection.
  • The findings contribute to a deeper understanding of non-classical resources in quantum information theory.