Ultimate Accuracy Limit of Quantum Pulse-Compression Ranging.

Radars use time-of-flight measurement to infer the range to a distant target from its return's round-trip range delay. They typically transmit a high time-bandwidth product waveform and use pulse-compression reception to simultaneously achieve satisfactory range resolution and range accuracy under a peak transmitted-power constraint. Despite the many proposals for quantum radar, none have delineated the ultimate quantum limit on ranging accuracy. We derive that limit through continuous-time quantum analysis and show that quantum illumination ranging-a quantum pulse-compression radar that exploits the entanglement between a high time-bandwidth product transmitted signal pulse and and a high time-bandwidth product retained idler pulse-achieves that limit. We also show that quantum illumination ranging offers mean-squared range-delay accuracy that can be tens of dB better than that of a classical pulse-compression radar of the same pulse bandwidth and transmitted energy.

Experimental Demonstration of Conjugate-Franson Interferometry.

Franson interferometry is a well-known quantum measurement technique for probing photon-pair frequency correlations that is often used to certify time-energy entanglement. We demonstrate, for the first time, the complementary technique in the time basis called conjugate-Franson interferometry. It measures photon-pair arrival-time correlations, thus providing a valuable addition to the quantum toolbox. We obtain a conjugate-Franson interference visibility of 96±1% without background subtraction for entangled photon pairs generated by spontaneous parametric down-conversion. Our measured result surpasses the quantum-classical threshold by 25 standard deviations and validates the conjugate-Franson interferometer (CFI) as an alternative method for certifying time-energy entanglement. Moreover, the CFI visibility is a function of the biphoton's joint temporal intensity, and is therefore sensitive to that state's spectral phase variation: something that is not the case for Franson interferometry or Hong-Ou-Mandel interferometry. We highlight the CFI's utility by measuring its visibilities for two different biphoton states: one without and the other with spectral phase variation, observing a 21% reduction in the CFI visibility for the latter. The CFI is potentially useful for applications in areas of photonic entanglement, quantum communications, and quantum networking.

Performance analysis of free-space quantum key distribution using multiple spatial modes.

In the diffraction-limited near-field propagation regime, free-space optical quantum key distribution (QKD) systems can employ multiple spatial modes to improve their key rate. This improvement can be effected by means of high-dimensional QKD or by spatial-mode multiplexing of independent QKD channels, with the latter, in general, offering higher key rates. Here, we theoretically analyze spatial-mode-multiplexed, decoy-state BB84 whose transmitter mode set is either a collection of phase-tilted, flat-top focused beams (FBs) or the Laguerre-Gaussian (LG) modes. Although for vacuum propagation the FBs suffer a QKD rate penalty relative to the LG modes, their potential ease of implementation make them an attractive alternative. Moreover, in the presence of turbulence, the FB modes may outperform the LG modes.

Entanglement-Assisted Communication Surpassing the Ultimate Classical Capacity.

Entanglement underpins a variety of quantum-enhanced communication, sensing, and computing capabilities. Entanglement-assisted communication (EACOMM) leverages entanglement preshared by communicating parties to boost the rate of classical information transmission. Pioneering theory works showed that EACOMM can enable a communication rate well beyond the ultimate classical capacity of optical communications, but an experimental demonstration of any EACOMM advantage remains elusive. In this Letter we report the implementation of EACOMM surpassing the classical capacity over lossy and noisy bosonic channels. We construct a high-efficiency entanglement source and a phase-conjugate quantum receiver to reap the benefit of preshared entanglement, despite entanglement being broken by channel loss and noise. We show that EACOMM beats the Holevo-Schumacher-Westmoreland capacity of classical communication by up to 16.3%, when both protocols are subject to the same power constraint at the transmitter. As a practical performance benchmark, we implement a classical communication protocol with the identical characteristics for the encoded signal, showing that EACOMM can reduce the bit-error rate by up to 69% over the same bosonic channel. Our work opens a route to provable quantum advantages in a wide range of quantum information processing tasks.

Room-temperature photonic logical qubits via second-order nonlinearities.

Recent progress in nonlinear optical materials and microresonators has brought quantum computing with bulk optical nonlinearities into the realm of possibility. This platform is of great interest, not only because photonics is an obvious choice for quantum networks, but also as a promising route to quantum information processing at room temperature. We propose an approach for reprogrammable room-temperature photonic quantum logic that significantly simplifies the realization of various quantum circuits, and in particular, of error correction. The key element is the programmable photonic multi-mode resonator that implements reprogrammable bosonic quantum logic gates, while using only the bulk χ(2) nonlinear susceptibility. We theoretically demonstrate that just two of these elements suffice for a complete, compact error-correction circuit on a bosonic code, without the need for measurement or feed-forward control. Encoding and logical operations on the code are also easily achieved with these reprogrammable quantum photonic processors. An extrapolation of current progress in nonlinear optical materials and photonic circuits indicates that such circuitry should be achievable within the next decade.

Single-photon frequency shifting with a quadrature phase-shift keying modulator.

Deterministic frequency manipulation of single photons is an essential tool for quantum communications and quantum networks. We demonstrate a 15.65 GHz frequency shift for classical and nonclassical light using a commercially available quadrature phase-shift keying modulator. The measured spectrum of frequency-shifted single photons indicates a high carrier-to-sideband ratio of 30 dB. We illustrate our frequency shifter's utility in quantum photonics by performing Hong-Ou-Mandel quantum interference between two photons whose initial frequency spectra overlap only partially, and showing visibility improvement from 62.7 to 89.1% after one of the photons undergoes a corrective frequency shift.

Nonparaxial phasor-field propagation.

Growing interest in non-line-of-sight (NLoS) imaging, colloquially referred to as "seeing around corners", has led to the development of phasor-field (P-field) imaging, wherein the field envelope of amplitude-modulated spatially-incoherent light is manipulated like an optical wave to directly probe a space that is otherwise shielded from view by diffuse scattering. Recently, we have established a paraxial theory for P-field imaging in a transmissive geometry that is a proxy for three-bounce NLoS imaging [J. Dove and J. H. Shapiro, Opt. Express27(13) 18016 (2019)]. Our theory, which relies on the Fresnel diffraction integral, introduces the two-frequency spatial Wigner distribution (TFSWD) to efficiently account for specularities and occlusions that may be present in the hidden space and cannot be characterized with P-field formalism alone. However, because the paraxial assumption is likely violated in many, if not most, NLoS scenarios, in the present paper we overcome that limitation by deriving a nonparaxial propagation formula for the P field using the Rayleigh-Sommerfeld diffraction integral. We also propose a Rayleigh-Sommerfeld propagation formula for the TFSWD and provide a derivation that is valid under specific partial-coherence conditions. Finally, we report a pair of differential equations that characterize free-space TFSWD propagation without restriction.

Speckled speckled speckle.

Speckle is the spatial fluctuation of irradiance seen when coherent light is reflected from a rough surface. It is due to light reflected from the surface's many nooks and crannies accumulating vastly discrepant time delays, spanning much more than an optical period, en route to an observation point. Although speckle with continuous-wave (cw) illumination is well understood, the emerging interest in non-line-of-sight (NLoS) imaging using coherent light has created the need to understand the higher-order speckle that results from multiple rough-surface reflections, viz., speckled speckle and speckled speckled speckle. Moreover, the recent introduction of phasor-field (P-field) NLoS imaging-which relies on amplitude-modulated coherent illumination-requires pushing beyond cw scenarios for speckle and higher-order speckle. In this paper, we take first steps in addressing the foregoing needs using a three-diffuser transmissive geometry that is a proxy for three-bounce NLoS imaging. In the small-diffusers limit, we show that the irradiance variances of cw and modulated nth-order speckle coincide and are (2n - 1)-times those of ordinary (first-order) speckle. The more important case for NLoS imaging, however, involves extended diffuse reflectors. For our transmissive geometry with extended diffusers, we treat third-order cw speckle and first-order modulated speckle. Our results there imply that speckle is unlikely to impede successful operation of coherent-illumination cw imagers, and they suggest that the same might be true for P-field imagers.

Paraxial phasor-field physical optics.

Phasor-field (P-field) imaging is a promising recent solution to the task of non-line-of-sight (NLoS) imaging, colloquially referred to as "seeing around corners." It consists of treating the oscillating envelope of amplitude-modulated, spatially-incoherent light as if it were itself an optical wave, akin to the oscillations of the underlying electromagnetic field. This resemblance enables traditional optical imaging strategies, e.g., lenses, to be applied to NLoS imaging tasks. To date, however, this ability has only been applied computationally. In this paper, we provide a rigorous mathematical demonstration that P-field imaging can be performed with physical optics, viz., that ordinary lenses can focus or project P fields through intervening diffusers-despite these diffusers' broadly dispersing the light passing through them-and that they can image scenes hidden by such diffusers. Hence NLoS imaging might be carried out via P-field physical optics without the nontrivial computational burden of prior NLoS techniques.

Single-End Adaptive Optics Compensation for Emulated Turbulence in a Bi-Directional 10-Mbit/s per Channel Free-Space Quantum Communication Link Using Orbital-Angular-Momentum Encoding.

A single-end adaptive-optics (AO) module is experimentally demonstrated to mitigate the emulated atmospheric turbulence effects in a bi-directional quantum communication link, which employs orbital angular momentum (OAM) for data encoding. A classical Gaussian beam is used as a probe to detect the turbulence-induced wavefront distortion in the forward direction of the link. Based on the detected wavefront distortion, an AO system located on one end of the link is used to simultaneously compensate for the forward and backward channels. Specifically, with emulated turbulence and when the probe is turned on, the mode purity of photons carrying OAM ℓ = 1 is improved by ~ 21 % with AO mitigation. We also measured the performance when encoding data using OAM {ℓ = -1, + 2} and {ℓ = -2, + 1} in the forward and backward channels, respectively, at 10 Mbit/s per channel with one photon per pulse on average. For this case, we found that the AO system could reduce the turbulence effects increased quantum-symbol-error-rate (QSER) by ~ 76 % and ~ 74 %, for both channels in the uni-directional and bi-directional cases, respectively. Similar QSER improvement is observed for the opposite direction channels in the bi-directional case.

Large-alphabet encoding for higher-rate quantum key distribution.

The manipulation of high-dimensional degrees of freedom provides new opportunities for more efficient quantum information processing. It has recently been shown that high-dimensional encoded states can provide significant advantages over binary quantum states in applications of quantum computation and quantum communication. In particular, high-dimensional quantum key distribution enables higher secret-key generation rates under practical limitations of detectors or light sources, as well as greater error tolerance. Here, we demonstrate high-dimensional quantum key distribution capabilities both in the laboratory and over a deployed fiber, using photons encoded in a high-dimensional alphabet to increase the secure information yield per detected photon. By adjusting the alphabet size, it is possible to mitigate the effects of receiver bottlenecks and optimize the secret-key rates for different channel losses. This work presents a strategy for achieving higher secret-key rates in receiver-limited scenarios and marks an important step toward high-dimensional quantum communication in deployed fiber networks.

Paraxial theory of phasor-field imaging.

The phasor field has been shown to be a valuable tool for non-line-of-sight imaging. We present a formal analysis of phasor-field imaging using paraxial wave optics. Then, we derive a set of propagation primitives-using the two-frequency, spatial Wigner distribution-that extend the purview of phasor-field imaging. We use these primitives to analyze a set of simple imaging scenarios involving occluded and unoccluded geometries with modulated and unmodulated light. These scenarios demonstrate how to apply the primitives in practice and reveal what kind of insights can be expected from them.

Indistinguishable single-mode photons from spectrally engineered biphotons.

We use pulsed spontaneous parametric down-conversion in KTiOPO 4, with a Gaussian phase-matching function and a transform-limited Gaussian pump, to achieve near-unity spectral purity in heralded single photons at telecommunication wavelength. Theory shows that these phase-matching and pump conditions are sufficient to ensure that a biphoton state with a circularly symmetric joint spectral intensity profile is transform limited and factorable. We verify the heralded-state spectral purity in a four-fold coincidence measurement by performing Hong-Ou-Mandel interference between two independently generated heralded photons. With a mild spectral filter we obtain an interference visibility of 98.4±1.1% which corresponds to a heralded-state purity of 99.2%. Our heralded photon source is potentially an essential resource for measurement-based quantum information processing and quantum network applications.

Qudit-Basis Universal Quantum Computation Using χ

We prove that universal quantum computation can be realized-using only linear optics and χ^{(2)} (three-wave mixing) interactions-in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ^{(2)} Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ^{(2)} interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection or subtraction, a technique enabled by χ^{(2)} interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool, in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.

Revealing hidden scenes by photon-efficient occlusion-based opportunistic active imaging.

The ability to see around corners, i.e., recover details of a hidden scene from its reflections in the surrounding environment, is of considerable interest in a wide range of applications. However, the diffuse nature of light reflected from typical surfaces leads to mixing of spatial information in the collected light, precluding useful scene reconstruction. Here, we employ a computational imaging technique that opportunistically exploits the presence of occluding objects, which obstruct probe-light propagation in the hidden scene, to undo the mixing and greatly improve scene recovery. Importantly, our technique obviates the need for the ultrafast time-of-flight measurements employed by most previous approaches to hidden-scene imaging. Moreover, it does so in a photon-efficient manner (i.e., it only requires a small number of photon detections) based on an accurate forward model and a computational algorithm that, together, respect the physics of three-bounce light propagation and single-photon detection. Using our methodology, we demonstrate reconstruction of hidden-surface reflectivity patterns in a meter-scale environment from non-time-resolved measurements. Ultimately, our technique represents an instance of a rich and promising new imaging modality with important potential implications for imaging science.

Efficient generation and characterization of spectrally factorable biphotons.

Spectrally unentangled biphotons with high single-spatiotemporal-mode purity are highly desirable for many quantum information processing tasks. We generate biphotons with an inferred heralded-state spectral purity of 99%, the highest to date without any spectral filtering, by pulsed spontaneous parametric downconversion in a custom-fabricated periodically-poled KTiOPO4 crystal under extended Gaussian phase-matching conditions. To efficiently characterize the joint spectral intensity of the generated biphotons at high spectral resolution, we employ a commercially available dispersion compensation module (DCM) with a dispersion equivalent to 100 km of standard optical fiber and with an insertion loss of only 2.8 dB. Compared with the typical method of using two temperature-stabilized equal-length fibers that incurs an insertion loss of 20 dB per fiber, the DCM approach achieves high spectral resolution in a much shorter measurement time. Because the dispersion amount and center wavelengths of DCMs can be easily customized, spectral characterization in a wide range of quantum photonic applications should benefit significantly from this technique.

Unity-Efficiency Parametric Down-Conversion via Amplitude Amplification.

We propose an optical scheme, employing optical parametric down-converters interlaced with nonlinear sign gates (NSGs), that completely converts an n-photon Fock-state pump to n signal-idler photon pairs when the down-converters' crystal lengths are chosen appropriately. The proof of this assertion relies on amplitude amplification, analogous to that employed in Grover search, applied to the full quantum dynamics of single-mode parametric down-conversion. When we require that all Grover iterations use the same crystal, and account for potential experimental limitations on crystal-length precision, our optimized conversion efficiencies reach unity for 1≤n≤5, after which they decrease monotonically for n values up to 50, which is the upper limit of our numerical dynamics evaluations. Nevertheless, our conversion efficiencies remain higher than those for a conventional (no NSGs) down-converter.

Optimum Mixed-State Discrimination for Noisy Entanglement-Enhanced Sensing.

Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources and, thus, nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise. Unfortunately, an implementation of the optimum quantum receiver that would reap QI's full performance advantage has remained elusive, owing to its having to deal with a huge number of very noisy optical modes. We show how sum-frequency generation (SFG) can be fruitfully applied to optimum multimode Gaussian-mixed-state discrimination. Applied to QI, our analysis and numerical evaluations demonstrate that our SFG receiver saturates QI's quantum Chernoff bound. Moreover, augmenting our SFG receiver with a feedforward (FF) mechanism pushes its performance to the Helstrom bound in the limit of low signal brightness. The FF-SFG receiver, thus, opens the door to optimum quantum-enhanced imaging, radar detection, state and channel tomography, and communication in practical Gaussian-state situations.

Photon-efficient imaging with a single-photon camera.

Reconstructing a scene's 3D structure and reflectivity accurately with an active imaging system operating in low-light-level conditions has wide-ranging applications, spanning biological imaging to remote sensing. Here we propose and experimentally demonstrate a depth and reflectivity imaging system with a single-photon camera that generates high-quality images from ∼1 detected signal photon per pixel. Previous achievements of similar photon efficiency have been with conventional raster-scanning data collection using single-pixel photon counters capable of ∼10-ps time tagging. In contrast, our camera's detector array requires highly parallelized time-to-digital conversions with photon time-tagging accuracy limited to ∼ns. Thus, we develop an array-specific algorithm that converts coarsely time-binned photon detections to highly accurate scene depth and reflectivity by exploiting both the transverse smoothness and longitudinal sparsity of natural scenes. By overcoming the coarse time resolution of the array, our framework uniquely achieves high photon efficiency in a relatively short acquisition time.

Computational multi-depth single-photon imaging.

We present an imaging framework that is able to accurately reconstruct multiple depths at individual pixels from single-photon observations. Our active imaging method models the single-photon detection statistics from multiple reflectors within a pixel, and it also exploits the fact that a multi-depth profile at each pixel can be expressed as a sparse signal. We interpret the multi-depth reconstruction problem as a sparse deconvolution problem using single-photon observations, create a convex problem through discretization and relaxation, and use a modified iterative shrinkage-thresholding algorithm to efficiently solve for the optimal multi-depth solution. We experimentally demonstrate that the proposed framework is able to accurately reconstruct the depth features of an object that is behind a partially-reflecting scatterer and 4 m away from the imager with root mean-square error of 11 cm, using only 19 signal photon detections per pixel in the presence of moderate background light. In terms of root mean-square error, this is a factor of 4.2 improvement over the conventional method of Gaussian-mixture fitting for multi-depth recovery.