Strongly non-quantitative classical information in quantum carriers

Abstract: A simple method to enhance the quality of communication is to send a carrier with its copies. Classical information theory says that information behaves quantitatively under copying. In other words, if a carrier is more informatic than another carrier, it remains so when they are compared with their copies. Using the lens of quantum mechanics, we challenge this accepted fact of classical information theory. Specifically, we examine two quantum systems parameterized differently by the same random variable such that the first system alone offers a more accurate guess about the variable in any figure of merit, while the two copies of the second system together do more in some figures of merit than the two copies of the original system. This finding unveils a conceptual discrepancy between classical information and its carrier, and implies the possibility of hiding classical information in a form of quantum information.