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A complete quantum generalization of microwave mixer theory is constructed for nonlinear single-particle tunnel junctions. The result represents a unification of the concepts used to describe these "classical" resistive mixers with the language of photon detection. Tunneling devices are predicted to undergo a transition from energy detectors to photon counters when operated at frequencies where the photon energy becomes comparable to the voltage scale of the dc nonlinearity. The small-signal video current response is found to approach one electron for each photon absorbed at high frequencies. In a heterodyne receiver, sufficiently nonlinear tunnel junctions are predicted to be capable of achieving the fundamental quantum noise limit for sensitivity in the detection of electromagnetic radiation. The theory presented here thus provides a framework for systematically extending the techniques of quantum electronics to considerably lower frequencies than are currently being exploited. Recent measurements of heterodyne mixer performance using superconductive tunneling devices are already beginning to approach quantum limited results at microwave and millimeter wave frequencies. Eventual application of tunnel barriers as photon detectors in the submillimeter and infrared spectral regions also appears to be possible, and the fast response times of such devices could give them an advantage over photoconductors even at the higher frequencies. The development of suitable nonlinear tunnel junctions contains the potential to bridge the present gap in quantum detectors between the infrared photon devices and microwave masers.