Error Probability Derivation in a Phonon-based Quantum Channel

Quantum communications are gaining more and more interest in the research community thanks to the recent advancements in nanotechnology. Indeed, quantum phenomena represent a natural direction for developing nanotechnology. The exploitation of quantum nature of information offers new potential solutions in the field of computing and networking, and extends the communication potentiality to levels that cannot be imagined in classical communication systems. Quantum communications can be realized in different ways. In this paper, we focus on the exploitation of quantum particles and quantum channels, in order to realize a data transmission system by means of phonons. First, we introduce the channel model of a phonon-based quantum system, and then derive the analysis of the error probability associated to such quantum channel. The application scenario is a biological environment, where phonons are exploited as information carriers. We have dealt a numerical evaluation in order to assess the performance of the quantum communication system. In particular, we have derived numerical results in terms of the error probability and the activity time, which represent how effective are phonons for communication purpose. We observe the frequency dependence of both error probability and activity time, thus allowing to tune the frequency for performance optimization.