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Register a new userSuper-Resolving Quantum Radar: Coherent-State Sources with Homodyne Detection Suffice to Beat the Diffraction Limit
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There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beers law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupled with a quantum homodyne detection scheme, provide both longitudinal and angular super-resolution much below the Rayleigh diffraction limit, with sensitivity at shot-noise in terms of the detected photon power. Our approach provides a template for the development of a complete super-resolving quantum radar system with currently available technology.
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We consider the moment operators of the observable (i.e. a semispectral measure or POM) associated with the balanced homodyne detection statistics, with paying attention to the correct domains of these unbounded operators. We show that the high amplitude limit, when performed on the moment operators, actually determines uniquely the entire statistics of a rotated quadrature amplitude of the signal field, thereby verifying the usual assumption that the homodyne detection achieves a measurement of that observable. We also consider, in a general setting, the possibility of constructing a measurement of a single quantum observable from a sequence of observables by taking the limit on the level of moment operators of these observables. In this context, we show that under some natural conditions (each of which is satisfied by the homodyne detector example), the existence of the moment limits ensures that the underlying probability measures converge weakly to the probability measure of the limiting observable. The moment approach naturally requires that the observables be determined by their moment operator sequences (which does not automatically happen), and it turns out, in particular, that this is the case for the balanced homodyne detector.
The Cram{e}r-Rao bound plays a central role in both classical and quantum parameter estimation, but finding the observable and the resulting inversion estimator that saturates this bound remains an open issue for general multi-outcome measurements. Here we consider multi-outcome homodyne detection in a coherent-light Mach-Zehnder interferometer and construct a family of inversion estimators that almost saturate the Cram{e}r-Rao bound over the whole range of phase interval. This provides a clue on constructing optimal inversion estimators for phase estimation and other parameter estimation in any multi-outcome measurement.
Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, $|alpha|ggfrac{d}{2pi}$, as a qudit --- a $d$-level quantum system --- in a state that is an even superposition of $d$ pseudo-number states. A pair of such coherent-state qudits can be prepared in maximally entangled state by generalized Controlled-$Z$ operation that is based on cross-Kerr nonlinearity, which can be weak for large $d$. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-$Z$ operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.
Performing homodyne detection at one port of squeezed-state light interferometer and then binarzing measurement data are important to achieve super-resolving and super-sensitive phase measurements. Here we propose a new data-processing technique by dividing the measurement quadrature into three bins (equivalent to a multi-outcome measurement), which leads to a higher improvement in the phase resolution and the phase sensitivity under realistic experimental condition. Furthermore, we develop a new phase-estimation protocol based on a combination of the inversion estimators of each outcome and show that the estimator can saturate the Cramer-Rao lower bound, similar to asymptotically unbiased maximum likelihood estimator.
Standard quantum state reconstruction techniques indicate that a detection efficiency of $0.5$ is an absolute threshold below which quantum interferences cannot be measured. However, alternative statistical techniques suggest that this threshold can be overcome at the price of increasing the statistics used for the reconstruction. In the following we present numerical experiments proving that quantum interferences can be measured even with a detection efficiency smaller than $0.5$. At the same time we provide a guideline for handling the tomographic reconstruction of quantum states based on homodyne data collected by low efficiency detectors.
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