Tsirelson inequalities: Detecting cheating and quantumness in a single framework

TL;DR

This paper demonstrates that Tsirelson inequalities can be used as a unified tool to detect quantum properties and cheating in classical games, offering a new perspective on quantumness in various systems.

Contribution

It introduces a unified framework using Tsirelson inequalities for detecting quantumness and cheating across different physical and classical systems.

Findings

Tsirelson inequalities can detect quantumness in diverse systems.

The framework can identify cheaters in classical shell games.

A geometric approach characterizes the space of conditional probabilities.

Abstract

Quantumness refers to the peculiar and counterintuitive characteristics exhibited by quantum systems. Tsirelson inequalities have emerged as a powerful tool in quantum theory to detect quantumness and entanglement of harmonic oscillators, spins undergoing uniform precession, and anharmonic systems. In this paper we harness the versatility of Tsirelson inequalities to address two distinct problems: detecting cheating in classic shell games and probing quantumness in spatially separated systems and harmonic oscillators. By adopting a black-box approach and a geometric characterization of the space of conditional probabilities, we demonstrate that Tsirelson inequalities can be used in both scenarios, enabling us to uncover quantum signatures and identify cheaters in a single unified framework. This connection provides an intuitive different perspective on quantumness of mechanical systems.