Communication and Measurement

Abstract

I discuss the process of measurement in the context of a communication system. The setting is a transmitter which encodes some physical object and sends it off, a receiver which measures some property of the transmitted physical object (TPO) in order to get some information, and some path between the transmitter and the receiver over which the TPO is sent. The object of the game here is to characterize the TPO, either as an end in itself (research), or to examine its potential for information transmittal (communication). If the TPO is a 'small' object then quantum mechanics is needed to play this game. In the course of this work, I hope to broaden the concept of measurement in quantum mechanics to include noisy measurements and incomplete measurements. I suggest that quantum density operators are logically associated with the transmitter and some portion of the path, and that quantum measurement operators are logically associated with the rest of the path and the receiver. Communication involves the overlap of a density operator and a measurement operator. That is, the fundamental conditional probability of the communication process is given by the trace of the product of a density operator and a measurement operator.