Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection.

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.

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.

Range dependence of an optical pulse position modulation link in the presence of background noise.

We analyze the information efficiency of a deep-space optical communication link with background noise, employing the pulse position modulation (PPM) format and a direct-detection receiver based on Geiger-mode photon counting. The efficiency, quantified using Shannon mutual information, is optimized with respect to the PPM order under the constraint of a given average signal power in simple and complete decoding scenarios. We show that the use of complete decoding, which retrieves information from all combinations of detector photocounts occurring within one PPM frame, allows one to achieve information efficiency scaling as the inverse of the square of the distance, i.e. proportional to the received signal power. This represents a qualitative enhancement compared to simple decoding, which treats multiple photocounts within a single PPM frame as erasures and leads to inverse-quartic scaling with the distance. We provide easily computable formulas for the link performance in the limit of diminishing signal power.

Visibility-Based Hypothesis Testing Using Higher-Order Optical Interference.

Many quantum information protocols rely on optical interference to compare data sets with efficiency or security unattainable by classical means. Standard implementations exploit first-order coherence between signals whose preparation requires a shared phase reference. Here, we analyze and experimentally demonstrate the binary discrimination of visibility hypotheses based on higher-order interference for optical signals with a random relative phase. This provides a robust protocol implementation primitive when a phase lock is unavailable or impractical. With the primitive cost quantified by the total detected optical energy, optimal operation is typically reached in the few-photon regime.

Quantum fingerprinting using two-photon interference.

We present a quantum fingerprinting protocol relying on two-photon interference which does not require a shared phase reference between the parties preparing optical signals carrying data fingerprints. We show that the scaling of the protocol, in terms of transmittable classical information, is analogous to the recently proposed and demonstrated scheme based on coherent pulses and first-order interference, offering comparable advantage over classical fingerprinting protocols without access to shared prior randomness. We analyze the protocol taking into account non-Poissonian photon statistics of optical signals and a variety of imperfections, such as transmission losses, dark counts, and residual distinguishability. The impact of these effects on the protocol performance is quantified with the help of Chernoff information.

Phase noise in collective binary phase shift keying with Hadamard words.

We analyze the effect of phase fluctuations in an optical communication scheme based on collective detection of sequences of binary coherent state symbols using linear optics and photon counting. When the phase noise is absent, the scheme offers qualitatively improved nonlinear scaling of the spectral efficiency with the mean photon number in the low-power regime compared to individual detection. We show that this feature, providing a demonstration of superaddivitity of accessible information in classical communication over quantum channels, is preserved if random phases imprinted on transmitted symbols fluctuate around a reference fixed over the sequence length.

Incoherent on-off keying with classical and non-classical light.

We analyze the performance of on-off keying (OOK) and its restricted version pulse position modulation (PPM) over a lossy narrowband optical channel under the constraint of a low average photon number, when direct detection is used at the output. An analytical approximation for the maximum PPM transmission rate is derived, quantifying the effects of photon statistics on the communication efficiency in terms of the g((2)) second-order intensity correlation function of the light source. Enhancement attainable through the use of sub-Poissonian light is discussed.

Matrix product states for quantum metrology.

We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with uncorrelated noise and is related to the elusive nature of the Heisenberg precision scaling in the asymptotic limit of a large number of probes.