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Analog-to-digital conversion at the receiver is known to be a stumbling block to the implementation of high data rate communications systems. It is desirable to answer the question of how the performance of a communications system is actually bounded when the analog-to-digital conversion stage is becoming its bottleneck. This paper studies the limits to communications with analog-to-digital conversion at the receiver, both from an information theoretic perspective as well as from a theoretical physics point of view. The maximum data rate that can be achieved for reliable transmission derives from the analog-to-digital conversion characteristics. Implications on optimal quantization and sampling rate are discussed. The principle of energy-time uncertainty leads to the fact that three quantization levels will allow for maximum data rate when operating at the frontiers of physics.