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Accessible information in molecular-scale systems: physical limits at small sampling volumes (Invited Paper)

We consider fundamental limits on information acquisition from localized regions of molecular-scale electronic systems. Our approach is based on a quantitative measure we call the volume accessible information, defined as the (Shannon) mutual information associated with the best possible quantum measurement that can access a system through a specified readout volume. Using results and techniques from quantum measurement theory, 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. An illustrative study of a model tight-binding system indeed reveals that the volume accessible information is sharply reduced at small sampling volumes, where the state distinguishability required for reliable information extraction is diminished.