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

Testing quantum mechanics: a statistical approach

As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited, how can we be sure that we are observing quantum behavior? This tutorial highlights some of the difficulties in such experimental tests of quantum mechanics, using optomechanics as the central example, and discusses how the issues can be resolved using techniques from statistics and insights from quantum information theory.Comment: v1: 2 pages; v2: invited tutorial for Quantum Measurements and Quantum Metrology, substantial expansion of v1, 19 pages; v3: accepted; v4: corrected some errors, publishe

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