Information as a physical quantity

Abstract

A new physical conception of classical information in quantum mechanical systems is explicated, critically assessed, and formalized in a quantitative measure. Observer-local referential (OLR) information—a shared physical property of entities accessible to a specified observer—is defined on the joint states of composite systems, distinguished from related conceptions of information, and tested against strict criteria that would simultaneously qualify it as a physical state quantity and as a meaningful measure of classical information. It is shown specifically to satisfy these criteria in the technological context of digital computation on quantum-physical substrates, where familiar alternatives—the von Neumann entropy and quantum mutual information (or correlation entropy)— fall short. The OLR conception provides a natural foundation for the fundamental physical description of information processing in digital computing systems, both because it defines information as a physical state quantity—placing it on an equal footing with other physical quantities appearing in such descriptions—and because it captures essential features of information in computational contexts that alternative physical conceptions do not. The OLR information measure enables straightforward and thoroughly physical quantification of digital information in general quantum systems and processes, enabling unambiguous determination of bounds on physical costs of generally noisy digital computation. More generally, OLR information offers a physical foundation for information that does not require the physical to be—ontologically or metaphorically—already informational.