# Fundamental Spacetime Representations of Quantum Antenna Systems
## 1 Introduction  
The main objective of this paper is to develop conceptual, physical, and mathematical foundations for quantum antenna theory based on a very broad approach to generic quantum fields produced and consumed by source and sink systems separated in spacetime. Quantum antenna technology is a recent emerging subfield within the larger and more fluid research area often referred to as quantum engineering, quantum technologies, or just quantum information processing. In particular, and within this subfield, we find that the main intention behind the desire for developing a new \"quantum antenna technology\" is to serve the needs of current and future quantum _communication_ systems [1, 2, 3, 4], where information is transmitted using quantum states [5, 6], regardless of whether digital data are encoded as classical bits or qbits [1, 7, 8, 9, 10], with obvious applications to physical-layer security [11, 12, 13, 14]. However, the peculiar system known as \"the quantum antenna\" mayalso perform functions other than mere information transmission in wireless quantum links, for example, quantum tomography, quantum state estimation, biophotonics, sensing, molecular communications, space exploration, and other applications [13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. We believe that quantum antenna theory and technology may be viewed as an attempt to synthesize three already established subfields: (1) classical antennas [27, 28], (2) optical nanoantennas [29, 30], and (3) quantum emitters [29, 31]. As such, a quantum antenna is often confused with one of these three topics. For example, occasionally, laser sources or photodiodes are treated as quantum antennas by some authors working in free space optical communications. This is _not_ what we understand by the term here. A laser source could constitute a part of the q-antenna system, while a larger part, for example a terahertz or an optical antenna [29, 32], may serve as a secondary reflector as in nanoantennas [30]. In addition, an atom emitting a photon after undergoing a transition from excited to ground states is not considered an \"antenna\" in this paper. Instead, we propose the following general definition:  
**Definition 1** (Antennas). : _By the term antenna, we follow classical antenna theory where the antenna system is defined as an externally controlled spatiotemporal current distribution capable of controlling the spatiotemporal properties of the radiation emitted by the antenna system._  
It will be seen that the most salient point in this definition is the emphasis on the following three features:  
1. The source is a controllable current distribution function of _both space and time_. 2. Ultimately, the source current is _externally_ controlled. 3. A spatiotemporal current distribution profile serving as a model for a quantum antenna source can control the _radiation_ proprieties in both space and time, and usually for near- and far-field scenarios as well. Hence, the existence of _spatiotemporal_, _externally_ controlled source current distributions capable of modifying its produced _radiation_ in both space _and_ time is the main content of antenna theory. Clearly enough, mainstream examples in quantum optics such as a laser source by itself, or an isolated atom undergoing a spontaneous emission of light, do not fall under a conceptual umbrella such as the one supplied by Definition 1, at least not naturally. However, such conventional quantum optical sources may still serve as essential _sub_-components of such systems. For example, probably, the most natural method to inject a controlled _time_ signal into a radiating nanostructure is through a modulated laser beam. However, controlling the _spatial_ distribution of the radiating _current_ excited by this time signal would require the use of _additional_ methods and objects; for instance, an optical antenna, or an engineered metamaterial, or an optimized array of point sources.