In this paper we derive the Clauser-Horne (CH) inequality for the full electron-counting statistics in a mesoscopic multiterminal conductor and discuss its properties. We first consider the idealized situation in which a flux of entangled electrons is generated by an entangler. Given a certain average number of incoming entangled electrons, the CH inequality can be evaluated for different numbers of transmitted particles. Strong violations occur when the number of transmitted charges on the two terminals is the same
(Q1=Q2), whereas no violation is found for ${Q}_{1}\ensuremath{\ne}{Q}_{2}.$ We then consider two actual setups that can be realized experimentally. The first one consists of a three terminal normal beam splitter and the second one of a hybrid superconducting structure. Interestingly, we find that the CH inequality is violated for the three terminal normal device. The maximum violation scales as
1/M and
1/M2 for the entangler and normal beam splitter, respectively,
2M being the average number of injected electrons. As expected, we find full violation of the CH inequality in the case of the superconducting system.
We discuss the Clauser–Horne (CH) inequality for electrons in mesoscopic systems formulated in terms of the full counting statistics (FCS). A derivation of such an inequality is provided for a prototype setup consisting of an entangler attached to two conducting wires, that brings pairs of spin-entangled electrons into spatially separated counters, where detection takes place. Violation of the CH inequality is analysed as a function of the various parameters characterizing the system. The effect of dephasing, which can occur in realistic wires, is also addressed. As expected, the extent of violation is monotonically suppressed by increasing dephasing strength. The CH inequality is finally applied to a three-arm normal-metallic beam splitter. Our results show that violation takes place even in the absence of interaction.
We have developed a new method to determine the photon statistics of a light source without the need for coincidence counting. Our method relies on using an asymmetric beam-splitter with intentional asymmetrical losses in a non-photon-number resolving detection system. We observe that the counts from one arm of the beam-splitter, when plotted as a function of the counts from the other arm, follow universal single-parameter curves that hint to the statistics of the photon source. We make a series of measurements on single photons detected from an attenuated laser source and show that the data clearly conforms to the universal curve established exclusively for coherent sources. We also show that the data cannot be fitted to the universal curve for thermal and photon-number sources.