Emulation of quantum experiments by conditional state preparation

Quantum states are able to carry more information to the receiver relatively to their classical counterparts. Such a property manifests itself in the EPR-type correlations, which cannot be explained classically and can be detected by violation of Bell inequalities, as well as in enhanced sensitivity of metrology with quantum probes (including optical field in squeezed and non-Poissonian states). This observation suggests that one can reproduce genuine quantum effects with classical states (such as coherent ones) by accompanying them with some additional information (attaching additional “labels”).
On the base of this idea, we propose an approach for “emulation” of quantum experiments by conditional preparation of classical (phase-averaged coherent) states. Here, the term “emulation” stands for reproducing expectation values of any observables by randomly preparing classical states from a predefined set with certain probabilities and postprocessing the measurement results by multiplying each outcome by a fixed coefficient with its sign being determined by the “label” (carrying 1 bit of classical information) attached to the prepared state.
The idea of the approach stems from data-pattern quantum tomography. The target non-classical state of optical field can be represented as a combination of coherent states with positive and negative weights (with the decomposition precision increasing when the number of states grows). A mixture of positive-weight or negative-weight coherent states can be generated just by sampling the coherent states randomly with the given probabilities. However non-negative probabilities cannot be used for combining the positive-weight and negative-weight states together. Therefore, one needs to use an additional “label” carrying the information about the sign of the coherent state in the decomposition of the target non-classical state. The price for the ability of classical emulation of non-classical effects is the excess noise introduced by sampling the label. By definition, any non-classical state would contain at least one negative-weight term in its decomposition, and the necessity to use the label sets the border between classical and non-classical states.
As an illustration of the approach, the schemes for emulation of non-classicality witnessing for a single-photon state, Hong-Ou-Mandel effect, and violation of Bell inequalities will be presented. Additionally, applications of the method to modeling of Hong-Ou-Mandel interference in radio-frequency domain and emulation of spatial resolution enhancement in antibunching imaging will be discussed. The developed approach is useful for deepening understanding of conceptual quantum-classical relations; for calibration of measurement setups without usage of the otherwise required non-classical light sources; and for educational purposes as an affordable tool for demonstration of quantum effects.