Sub-Rayleigh characterization of a binary source by spatially demultiplexed coherent detection.

We investigate theoretically coherent detection implemented simultaneously on a set of mutually orthogonal spatial modes in the image plane as a method to characterize properties of a composite thermal source below the Rayleigh limit. A general relation between the intensity distribution in the source plane and the covariance matrix for the complex field amplitudes measured in the image plane is derived. An algorithm to estimate parameters of a two-dimensional symmetric binary source is devised and verified using Monte Carlo simulations to provide super-resolving capability for a high ratio of signal to detection noise (SNR). Specifically, the separation between two point sources can be meaningfully determined down to SNR-1/2 in the length unit determined by the spatial spread of the transfer function of the imaging system. The presented algorithm is shown to make a nearly optimal use of the measured data in the sub-Rayleigh region.

Experimental detection of entanglement with optimal-witness families.

We report an experiment in which one determines, with least tomographic effort, whether an unknown two-photon polarization state is entangled or separable. The method measures whole families of optimal entanglement witnesses. We introduce adaptive measurement schemes that greatly speed up the entanglement detection. The experiments are performed on states of different ranks, and we find good agreement with results from computer simulations.

Quantum metrology with imperfect measurements.

The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections-with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.