2. States, Observables, Statistics

Alfredo Luis

Nonclassicality cannot be a single-observable property, since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior of light states from the joint statistics arising in the practical measurement of multiple observables. Beside embracing previous approaches, this protocol can disclose nonclassical features for standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. When combined with other criteria, this would imply that every light state is nonclassical.

Bernd Thaller

Yoon-Ho Kim, Warren P. Grice

Two-photon interference effects and correlated-photon statistics have traditionally been observed in the coincidence detection rate between two detectors. Here, we report observations of correlated-photon statistics, which are due to two-photon entanglement and interference, in the single-photon detection rate. The observed effects are explained by considering all possible photon number states that reach the detector, rather than considering just the state post-selected by the coincidence circuit.

CHRISTOF WETTERICH

Abstract We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated subsystem. The “coarse graining of the information” to micro‐states implies probabilistic observables. For two‐level probabilistic observables only a probability for finding the values one or minus one can be given for any micro‐state, while such observables could be realized as classical observables with sharp values on a substate level. For a continuous family of micro‐states parameterized by a sphere all the quantum mechanical laws for a two‐state system follow under the assumption that the purity of the ensemble is conserved by the time evolution. The correlation functions of quantum mechanics correspond to the use of conditional correlation functions in classical statistics. We further discuss the classical statistical realization of entanglement within a system corresponding to four‐state quantum mechanics. We conclude that quantum mechanics can be derived from a classical statistical setting with infinitely many micro‐states.