Some Common Aspects of Quantum and Classical Interferences

In quantum information theory, the particles are characterized by wave behavior where they can be described by particle-wave duality, from this perspective, the waves phenomena were studied theoretically and experimentally for quantum particles such as diffraction and interferences. In the other hand, the classical electromagnetic and acoustics fields are described by wave forms where all wave phenomena are possible including diffraction, refraction and scattering. Focusing on interferences where the superposition principle is valid for both quantum and classical interferences, we present in this paper, some common properties between the quantum interferences and particular case of classical interferences. Based on far field and narrowband classical interferences, the interactions between elementary wave forms are treated using array signal processing, where angular interferometry of wave fields using closely sensors or antennas, permit to localize and estimate the characteristics of the far field sources. Based on the geometry of the displacement of the isotropic and identical antennas and the planar shape of the wave front passing near the array, we present some mathematical common concepts between quantum and classical interferences starting from wave propagation equation to the Von Neumann entropy, we present a detailed description of similarities between the two branches using some tools of operator theory. In the last part, we present a numerical simulation where we show that the introduction of the quantum entropy on classical system of antennas-sources permit to identify different phases of the system with respect to the signal to noise ratio.