Quantum Direct-Sequence Spread-Spectrum CDMA Communication Systems: Mathematical Foundations

Abstract

This article describes the fundamental principles and mathematical foundations of quantum direct-sequence spread-spectrum code division multiple-access communication systems. The evolution of quantum signals through the quantum direct-sequence spread-spectrum multiple-access communication system is carefully characterized by a novel approach called the decomposition of creation operators. In this methodology, the creation operator of the transmitted quantum signal is decomposed into the chip-time interval creation operators, each of which is defined over the duration of a chip. These chip-time interval creation operators are the invariant building blocks of the spread-spectrum quantum communication systems. With the aid of the proposed chip-time decomposition approach, we can find closed-form relations for quantum signals at the receiver of such a quantum communication system. Furthermore, this article details the principles of narrowband filtering of quantum signals required at the receiver, a crucial step in designing and analyzing quantum communication systems. We show, that by employing coherent states as the transmitted quantum signals, the interuser interference appears as an additive term in the magnitude of the output coherent (Glauber) state, and the output of the quantum communication system is a pure quantum signal. On the other hand, if the transmitters utilize particle-like quantum signals (Fock states) such as single-photon states, the entanglement effect can arise at the receivers. The important techniques developed in this article are expected to have far-reaching implications for various applications in the exciting field of quantum communications and quantum signal processing.