Quantum Correlations of Photons and Qudit States

Abstract

We present briefly the historical aspects of studying the properties of light including both the classical theory of light based on the electromagnetic wave picture and the quantum corpuscular interpretation of light based on the notion of photons. We consider vibrations of electric and magnetic fields in light waves and quantum correlations described by the Heisenberg and Schrodinger–Robertson uncertainty relations valid for any vibrations in connection with specific statistical properties of coherent light and squeezed light. We review the qubit and qudit states and the new uncertainty relation for entropy and energy for qudit systems. We discuss the dynamical (nonstationary) Casimir effect providing a vacuum generator of squeezed photons based on the technique of superconducting circuits realized by Josephson junctions. We demonstrate new entropic inequalities for two qubits (polarization states of two photons) and hidden correlations of noncomposite quantum systems (quantum roulette).