Nonclassicality of states and measurements by breaking classical bounds on statistics

TL;DR

This paper presents simple, practical tests to identify quantum states and measurements by violating classical statistical bounds, applicable across various systems without complex analysis.

Contribution

It introduces straightforward procedures for detecting nonclassicality through classical bound violations, independent of traditional quantum signatures.

Findings

Effective nonclassicality detection across diverse systems

Minimal data analysis required for conclusive results

Applicable to both ideal and noisy measurements

Abstract

We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are independent of other typical quantum signatures such as sub-Poissonian statistics, quadrature squeezing, or oscillatory statistics. This approach can be equally well applied to very diverse situations such as single- and two-mode fields, observables with continuous and discrete spectra, finite- and infinite-dimensional systems, and ideal and noisy measurements.