What theorem states that if a source can be transmitted over a channel in any way, it can be transmitted using a binary interface between source and channel?

The source/channel separation theorem is indeed the correct answer because it establishes the principle that it is possible to separate the processes of source coding and channel coding. This means that if a source provides data, it can be encoded in such a way that it can be effectively transmitted over a communication channel using a binary interface. This theorem affirms that the source information can first be compressed or encoded optimally and then transmitted over the channel without losing the ability to recover the original data.

This concept is foundational in information theory and underpins many modern communication methods. By asserting that the source can be processed independently from the transmission medium, it allows for more flexible and efficient communication strategies, especially when working with binary systems.

In contrast, other options, while significant in their own right, do not directly address the specific relationship between source encoding and channel transmission as brought forth by the source/channel separation theorem. For instance, Nyquist's theorem relates to the maximum data transmission rate of a channel without ISI (inter-symbol interference), and Shannon's source coding theorem focuses on the limits of lossless compression. Information theory itself encompasses the broader study of how information is quantified, stored, and communicated but does not specifically delineate the separation of source and channel operations.