What is data processing inequality?

Data processing inequality is a principle in information theory that states that if data is processed or transformed in any way, it cannot become more informative or carry more information than the original data. More specifically, the principle states that if X and Y are two random variables related by a deterministic function f, then the amount of information contained in X is at least as much as the amount of information contained in Y: I(X;Y) <= I(X;f(Y)). This principle has important implications for information security, data analysis, and communication systems, among other fields. The data processing inequality ensures that the privacy of data can be preserved even when processing or transformation takes place, as long as the original data is not disclosed.