Given an experimental set-up and a fixed number of measurements, how should one take data in order to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached
by Kosut et al. [arXiv:quant-ph/0411093v1]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of minimal tomography. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. We find that these two designs are generally similar. Monte-Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.
We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite
photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e. the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.
By using a systematic optimization approach we determine quantum states of light with definite photon number leading to the best possible precision in optical two mode interferometry. Our treatment takes into account the experimentally relevant situa
tion of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.
We present Spitzer infrared, GALEX UV, and SDSS and SARA optical images of the peculiar interacting galaxy pair Arp 285 (NGC 2856/4), and compare with a new numerical model of the interaction. We estimate the ages of clumps of star formation in these
galaxies using population synthesis models, carefully considering the uncertainties on these ages. This system contains a striking example of `beads on a string: a series of star formation complexes ~1 kpc apart. These `beads are found in a tail-like feature that is perpendicular to the disk of NGC 2856, which implies that it was formed from material accreted from the companion NGC 2854. The extreme blueness of the optical/UV colors and redness of the mid-infrared colors implies very young stellar ages (~4 - 20 Myrs) for these star forming regions. Spectral decomposition of these `beads shows excess emission above the modeled stellar continuum in the 3.6 micron and 4.5 micron bands, indicating either contributions from interstellar matter to these fluxes or a second older stellar population. These clumps have -12.0 < M(B) < -10.6, thus they are less luminous than most dwarf galaxies. Our model suggests that bridge material falling into the potential of the companion overshoots the companion. The gas then piles up at apo-galacticon before falling back onto the companion, and star formation occurs in the pile-up. A luminous (M(B) ~ -13.6) extended (FWHM ~ 1.3 kpc) `bright spot is visible at the northwestern edge of the NGC 2856 disk, with an intermediate stellar population (400 - 1500 Myrs). Our model suggests that this feature is part of a expanding ripple-like `arc created by an off-center ring-galaxy-like collision between the two disks.
