# Error Performance of Amplitude Shift Keying-Type Asymmetric Quantum Communication Systems
## 1 Introduction  
Entanglement [1] is an important phenomenon for quantum protocols. Entanglement is a nonlocal correlation that works with multiple quantum systems. This correlation can be maintained regardless of the distance between these multiple quantum systems. The quantum cryptographic protocol called E91 [2], quantum superdense coding [3], and quantum teleportation [4], which were all proposed in the 1990s, are well known as quantum communication protocols that apply entanglement. In addition, quantum illumination [5] and quantum reading [6], which are quantum metrology protocols based on entanglement and were proposed around 2010, have also been attracting increasing attention in recent years. Many of the quantum communication protocols described above that use entanglement belong to the class of symmetric communication systems. Symmetric communication systems have the same transmission capability, regardless of the direction of communication. In contrast, asymmetric communication systems have different transmission capabilities that depend on the direction of communication (e.g., [7, 8]). The differences in transmission capability in this case are caused by the differences between the physical resources that can be used on the two sides of the communication process. However, as far as we know, there are no asymmetric communication systems which essentially utilize quantum mechanical phenomena such as entanglement. With this in mind, we define the following: asymmetric systems using quantum and classical communication protocols are called asymmetric quantum communication (AQC) systems and asymmetric classical communication (ACC) systems, respectively. In this paper, we consider the quantum communication protocols with entanglement. Typical examples of ACC systems include terrestrial-to-satellite communications, communication between a mobile device and a cellular base station, and communication between an Internet of Things (IoT) device and an IoT base station. For example, in an IoT-based ACC system, there is a major differencebetween the transmission capabilities of a small battery-driven IoT device--where the battery is replaced once every few years and the microprocessor unit can only perform simple calculation processes--and that of a base station with an abundant power supply and high processing capacity. In this work, the side with the low transmission capability, e.g., satellites, mobile phones, and IoT devices, is called Alice, and the side with the high transmission capability, e.g., ground base stations, mobile phone base stations, and IoT base stations, is called Bob. Taking an IoT-based ACC system as an example, the usage scenario of that is considered as a simple model in this paper follows: (1) Bob (the IoT base station) tells Alice (the IoT device) whether to sense the physical environment; (2) if yes, Alice senses the physical environment and transmits the corresponding data to Bob. In general, information leakage is prone to occur in the channel of (2), and the system must perform some communication protocols, such as lightweight cryptography. One of the security problems for the asymmetric communication system can be described as follows: the low processing capacity struggles to always provide a high security level for the data transmitted from such an IoT device, because the frequency of upgrading the device may be low and the development of code breaking technique is fast. We aimed to develop a new AQC system to improve the reliability and security of communications from Alice to Bob, and also to reduce Alice's energy costs by introducing entanglement into the asymmetric communication system. This paper represents the first step in this research. To develop the required AQC system, it will be necessary to clarify the effects of deterioration of the quantum effects in the various channels with respect to the entangled state. Reference [9] dealt with the quantum channel discrimination problem using beam splitters with reflectivities of \(R_{0}\) and \(R_{1}(0\leq R_{0}<R_{1}\leq 1)\).