Continuous-variable Bell nonlocality with biphotons produced by spontaneous parametric down-conversion

Abstract

We revisit a continuous-variable version of the Clauser-Horne-Shimony-Holt inequality with sign binning, first proposed by Bell [J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 1st ed. (Cambridge University, New York, 1987); Ann. N.Y. Acad. Sci. 480, 263 (1986)]. To explore Bell nonlocality, we use a biphoton effective wave function resulting from a type-I spontaneous parametric down-conversion process. After reviewing the approximations involved in the production and time evolution of such biphotons, we judiciously choose a series expansion for the sinc function part of the biphoton wave function in order to integrate the Wigner function. We conclude that we can qualitatively achieve Bell nonlocality within a regime in which the twin photons are described.