Witnessing the survival of time-energy entanglement through biological tissue and scattering media.

We demonstrate the preservation of the time-energy entanglement of near-IR photons through thick biological media (≤1.55 mm) and tissue (≤ 235 µm) at room temperature. Using a Franson-type interferometer, we demonstrate interferometric contrast of over 0.9 in skim milk, 2% milk, and chicken tissue. This work supports the many proposed opportunities for nonclassical light in biological imaging and analyses from sub-shot noise measurements to entanglement-enhanced fluorescence imaging, clearly indicating that the entanglement characteristics of photons can be maintained even after propagation through thick, turbid biological samples.

Compressively sampling the optical transmission matrix of a multimode fibre.

The measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields, including optical communications, micro-manipulation, and computing. In many cases, the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore, applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. Here, we explore how these measurement requirements can be relaxed using the framework of compressive sensing, in which the incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity. We show that in this case, imaging is still possible using TMs reconstructed at compression ratios down to ∼1% (eight probe measurements). This compressive TM sampling strategy is quite general and may be applied to a variety of other scattering samples, including diffusers, thin layers of tissue, fibre optics of any refractive profile, and reflections from opaque walls. These approaches offer a route towards the measurement of high-dimensional TMs either quickly or with access to limited numbers of measurements.

Frequency-modulated continuous-wave LiDAR compressive depth-mapping.

We present an inexpensive architecture for converting a frequency-modulated continuous-wave LiDAR system into a compressive-sensing based depth-mapping camera. Instead of raster scanning to obtain depth-maps, compressive sensing is used to significantly reduce the number of measurements. Ideally, our approach requires two difference detectors. Due to the large flux entering the detectors, the signal amplification from heterodyne detection, and the effects of background subtraction from compressive sensing, the system can obtain higher signal-to-noise ratios over detector-array based schemes while scanning a scene faster than is possible through raster-scanning. Moreover, by efficiently storing only 2m data points from m < n measurements of an n pixel scene, we can easily extract depths by solving only two linear equations with efficient convex-optimization methods.

Short-wave infrared compressive imaging of single photons.

We present a short-wave infrared (SWIR) single photon camera based on a single superconducting nanowire single photon detector (SNSPD) and compressive imaging. We show SWIR single photon imaging at a megapixel resolution with a low signal-to-background ratio around 0.6, show SWIR video acquisition at 20 frames per second and 64x64 pixel video resolution, and demonstrate sub-nanosecond resolution time-of-flight imaging. All scenes were sampled by detecting only a small number of photons for each compressive sampling matrix. In principle, our technique can be used for imaging faint objects in the mid-IR regime.

Quantum enigma machine: Experimentally demonstrating quantum data locking.

Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure.

Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution.

We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 million-dimensional image in less than 10 minutes. Within a subspace of that image exists a 3.2 million-dimensional bi-photon probability distribution. In addition, we demonstrate how the marginal distributions can aid in the accuracy of joint space distribution reconstructions.

Compressive wavefront sensing with weak values.

We demonstrate a wavefront sensor that unites weak measurement and the compressive-sensing, single-pixel camera. Using a high-resolution spatial light modulator (SLM) as a variable waveplate, we weakly couple an optical field's transverse-position and polarization degrees of freedom. By placing random, binary patterns on the SLM, polarization serves as a meter for directly measuring random projections of the wavefront's real and imaginary components. Compressive-sensing optimization techniques can then recover the wavefront. We acquire high quality, 256 × 256 pixel images of the wavefront from only 10,000 projections. Photon-counting detectors give sub-picowatt sensitivity.

Simultaneous measurement of complementary observables with compressive sensing.

The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the entropic formulation of the uncertainty principle. Traditionally, uncertainly relations correspond to resolution limits; increasing a detector's position sensitivity decreases its momentum sensitivity and vice versa. However, this is not required in general; for example, position information can instead be extracted at the cost of noise in momentum. Using random, partial projections in position followed by strong measurements in momentum, we efficiently determine the transverse-position and transverse-momentum distributions of an unknown optical field with a single set of measurements. The momentum distribution is directly imaged, while the position distribution is recovered using compressive sensing. At no point do we violate uncertainty relations; rather, we economize the use of information we obtain.

Photon counting compressive depth mapping.

We demonstrate a compressed sensing, photon counting lidar system based on the single-pixel camera. Our technique recovers both depth and intensity maps from a single under-sampled set of incoherent, linear projections of a scene of interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional reconstructions are required to image a three-dimensional scene. We demonstrate intensity imaging and depth mapping at 256 × 256 pixel transverse resolution with acquisition times as short as 3 seconds. We also show novelty filtering, reconstructing only the difference between two instances of a scene. Finally, we acquire 32 × 32 pixel real-time video for three-dimensional object tracking at 14 frames-per-second.