Nonclassicality of states and measurements by breaking classical bounds on statistics

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.