Accessible information from molecular-scale volumes in electronic systems: Fundamental physical limits

We consider fundamental limits on accessible information from molecular-scale volumes in electronic systems. Our approach is based on a quantitative measure—the volume accessible information—which we define as the Shannon mutual information associated with the best possible quantum measurement that can access a system through a specified readout volume. Specifically, we obtain a general expression for an upper bound on the volume accessible information that depends only on the manner in which information is encoded in electron states and specification of the readout volume. This bound is obtained within a tight-binding framework for simplicity and compatibility with atomistic descriptions of molecular-scale electronic systems. As an illustration, we study the volume accessible information bound for measurements accessing finite segments of long polyparaphenylene (PPP) molecules with binary information encoded in the states of electrons in the lowest unoccupied molecular orbital band. Evaluation of this bound reveals severe limits on the amount of information accessible from measurements on short PPP chain segments, where the state distinguishability required for reliable information extraction is diminished.