# Non-classical Correlations in n-Cycle Setting

## TL;DR

This paper investigates non-classical correlations in n-cycle scenarios, analyzing inequalities, quantum violations, and simulation of generalized boxes, providing criteria for classical simulation and extending to continuous variables.

## Contribution

It introduces criteria for optimal classical simulation of KS boxes, analyzes non-contextuality inequalities for all n, and extends these inequalities to continuous variables.

## Key findings

- Criteria for classical simulation of KS boxes of arbitrary dimension
- Quantum violations of n-cycle non-contextuality inequalities for all n
- Extension of inequalities to continuous variable systems

## Abstract

We explore non-classical correlations in n-cycle setting. In particular, we focus on correlations manifested by Kochen-Specker-Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu-Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the continuous variable case. Furthermore, we simulate a generalized PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research.