This paper is concerned with the problem of finding the structure and performance of the receiver that yields the best performance in the reception of signals that are described quantum-mechanically. The principles of statistical detection and estimation theory are discussed, with the laws of quantum mechanics taken into account. Several specific communication systems of practical interest are studied as examples of applying these principles. Basic concepts in quantum mechanics that are needed in these discussions are briefly reviewed.
We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the mechanical oscillator, which is prepared in a thermal state. We show how the optical field acquires a phase depending on the anharmonicity. Remarkably, one only needs small initial cooling of the mechanical motion to probe even small anharmonicities. Finally, by applying tools from quantum estimation theory, we calculate the ultimate bound on the estimation precision posed by quantum mechanics and compare it with the precision obtainable with feasible measurements such as homodyne and heterodyne detection on the cavity field. In particular we demonstrate that homodyne detection is nearly optimal in the limit of a large number of photons of the field and we discuss the estimation precision of small anharmonicities in terms of its signal-to-noise ratio.
This work presents a probability theory of coincidence detection to address the detection limit of time-correlated photon sources. We use Bayes’ theorem to model instruments as a noisy communication channel and apply statistical inference to identify the minimum detectable coincidence rate. Photon triplet generation is considered as a case study to illustrate the application of coincidence detection theory for time-correlated photon sources that are based on spontaneous parametric down-conversion. A triplet generation rate of 1–100 Hz is required for source characterization performed over 1–72 hours using superconducting nanowire single-photon detectors. We envision the connection between Bayes’ theorem and coincidence detection opens up a new avenue for applying signal processing techniques available in information theory to photon coincidence measurements.