Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing. II. Applications to atomic magnetometry and Hardy's paradox

The quantum smoothing theory [Tsang, Phys. Rev. Lett. 102, 250403 (2009); Phys. Rev. A, in press (e-print arXiv:0906.4133)] is extended to account for discrete jumps in the classical random process to be estimated, discrete variables in the quantum system, such as spin, angular momentum, and photon number, and Poissonian measurements, such as photon counting. The extended theory is used to model atomic magnetometers and study Hardy's paradox in phase space. In the phase-space picture of Hardy's proposed experiment, the negativity of the predictive Wigner distribution is identified as the culprit of the disagreement between classical reasoning and quantum mechanics.Comment: 11 pages, 3 figure

Quantum metrology with open dynamical systems

This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical force sensing. When optical loss is present, these bounds are found to obey shot-noise scalings for arbitrary quantum states of light under certain realistic conditions, thus ruling out the possibility of asymptotic Heisenberg error scalings with respect to the average photon flux under those conditions. The proposed bounds are expected to be approachable using current quantum optics technology.Comment: v1: submitted to ISIT 2013, v2: updated with new results on detection bounds, v3: minor update, submitted, v4: accepted by New J. Phy

Volterra filters for quantum estimation and detection

The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to quantum estimation and detection based on Volterra filters. Volterra filters have a clear hierarchy of computational complexities and performances, depend only on finite-order correlation functions, and are applicable to systems with no simple Markovian model. These features make Volterra filters appealing alternatives to optimal nonlinear protocols for the inference and control of complex quantum systems. Applications of the first-order Volterra filter to continuous-time quantum filtering, the derivation of a Heisenberg-picture uncertainty relation, quantum state tomography, and qubit readout are discussed.Comment: v2: added more in-depth discussions, more references, and a qubit readout example with two new figures. Improved presentation; v3: extended and publishe

Mismatched Quantum Filtering and Entropic Information

Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state preparation, quantum metrology, and quantum control. If the filter assumes a nominal model that differs from reality, however, the estimation accuracy is bound to suffer. Here I derive identities that relate the excess error caused by quantum filter mismatch to the relative entropy between the true and nominal observation probability measures, with one identity for Gaussian measurements, such as optical homodyne detection, and another for Poissonian measurements, such as photon counting. These identities generalize recent seminal results in classical information theory and provide new operational meanings to relative entropy, mutual information, and channel capacity in the context of quantum experiments.Comment: v1: first draft, 8 pages, v2: added introduction and more results on mutual information and channel capacity, 12 pages, v3: minor updates, v4: updated the presentatio

Quantum Imaging beyond the Diffraction Limit by Optical Centroid Measurements

I propose a quantum imaging method that can beat the Rayleigh-Abbe diffraction limit and achieve de Broglie resolution without requiring a multiphoton absorber as the detector. Using the same non-classical states of light as those for quantum lithography, the proposed method requires only intensity measurements, followed by image post-processing, to produce the same complex image patterns as those in quantum lithography. The method is expected to be experimentally realizable using current technology.Comment: 4 pages, 2 figures; v2: accepted by PRL, see also the accompanying Viewpoint commentary by Anisimov and Dowling [Physics 2, 52 (2009), http://physics.aps.org/articles/v2/52