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Jeffrey H. Shapiro

Publications and source records attributed to Jeffrey H. Shapiro.

At least 37 records · Page 2Linked to original sources
arXiv2021

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 because it may be the only feasible route to quantum information processing at room temperature. We introduce a paradigm for room-temperature photonic quantum logic that significantly simplifies the realization of various quantum circuits, and in particular, of error correction. It uses only the strongest available bulk nonlinearity, namely the $χ^{(2)}$ nonlinear susceptibility. The key element is a three-mode resonator that implements programmable bosonic quantum logic gates. We show 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. An extrapolation of current progress in nonlinear optical materials and photonic circuits indicates that such circuitry should be achievable within the next decade.

quant-ph↗
arXiv2020

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 ($\mathcal{P}$-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 $\mathcal{P}$-field imaging in a transmissive geometry that is a proxy for three-bounce NLoS imaging [J. Dove and J. H. Shapiro, Opt. Express {\bf 27}(13) 18016--18037 (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 $\mathcal{P}$-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 $\mathcal{P}$ 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.

physics.optics↗
arXiv2020

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 ($\mathcal{P}$-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 $n$th-order speckle coincide and are $(2^n-1)$-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 $\mathcal{P}$-field imagers.

physics.optics↗
arXiv2020

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.

physics.optics↗
arXiv2019

The Quantum Illumination Story

Superposition and entanglement, the quintessential characteristics of quantum physics, have been shown to provide communication, computation, and sensing capabilities that go beyond what classical physics will permit. It is natural, therefore, to explore their application to radar, despite the fact that decoherence---caused by the loss and noise encountered in radar sensing---destroys these fragile quantum properties. This paper tells the story of "quantum illumination", an entanglement-based approach to quantum radar, from its inception to its current understanding. Remarkably, despite loss and noise that destroy its initial entanglement, quantum illumination does offer a target-detection performance improvement over a classical radar of the same transmitted energy. A realistic assessment of that improvement's utility, however, shows that its value is severely limited. Nevertheless, the fact that entanglement can be of value on an entanglement-breaking channel---the meta-lesson of the quantum illumination story---should spur continued research on quantum radar.

quant-ph↗
arXiv2019

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.

physics.optics↗
arXiv2019

Secret key distillation across a quantum wiretap channel under restricted eavesdropping

The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret key distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Further, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, e.g., to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.

cs.IT↗
arXiv2018

Security-proof framework for two-way Gaussian quantum-key-distribution protocols

Two-way Gaussian protocols have the potential to increase quantum key distribution (QKD) protocols' secret-key rates by orders of magnitudes~[Phys.~Rev.~A {\bf 94}, 012322 (2016)]. Security proofs for two-way protocols, however, are underdeveloped at present. In this paper, we establish a security proof framework for the general coherent attack on two-way Gaussian protocols in the asymptotic regime. We first prove that coherent-attack security can be reduced to collective-attack security for all two-way QKD protocols. Next, we identify two different constraints that each provide intrusion parameters which bound an eavesdropper's coherent-attack information gain for any two-way Gaussian QKD protocol. Finally, we apply our results to two such protocols.

quant-ph↗
arXiv2018

Resource theory of non-Gaussian operations

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is non-increasing under the set of free super-operations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (1) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition and all Gaussian-dilatable non-Gaussian channels; and (2) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian-dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

quant-ph↗
arXiv2018

Distributed Quantum Sensing Using Continuous-Variable Multipartite Entanglement

Distributed quantum sensing uses quantum correlations between multiple sensors to enhance the measurement of unknown parameters beyond the limits of unentangled systems. We describe a sensing scheme that uses continuous-variable multipartite entanglement to enhance distributed sensing of field-quadrature displacement. By dividing a squeezed-vacuum state between multiple homodyne-sensor nodes using a lossless beam-splitter array, we obtain a root-mean-square (rms) estimation error that scales inversely with the number of nodes (Heisenberg scaling), whereas the rms error of a distributed sensor that does not exploit entanglement is inversely proportional to the square root of number of nodes (standard quantum limit scaling). Our sensor's scaling advantage is destroyed by loss, but it nevertheless retains an rms-error advantage in settings in which there is moderate loss. Our distributed sensing scheme can be used to calibrate continuous-variable quantum key distribution networks, to perform multiple-sensor cold-atom temperature measurements, and to do distributed interferometric phase sensing.

quant-ph↗
arXiv2018

Qudit-Basis Universal Quantum Computation using $χ^{(2)}$ Interactions

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 $\mathfrak{u}(3)$ 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/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.

quant-ph↗
arXiv2018

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 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.

stat.AP↗
arXiv2017

Experimental Quantum Key Distribution at 1.3 Gbit/s Secret-Key Rate over a 10-dB-Loss Channel

Quantum key distribution (QKD) enables unconditionally secure communication ensured by the laws of physics, opening a promising route to security infrastructure for the coming age of quantum computers. QKD's demonstrated secret-key rates (SKRs), however, fall far short of the gigabit-per-second rates of classical communication, hindering QKD's widespread deployment. QKD's low SKRs are largely due to existing single-photon-based protocols' vulnerability to channel loss. Floodlight QKD (FL-QKD) boosts SKR by transmitting many photons per encoding, while offering security against collective attacks. Here, we report an FL-QKD experiment operating at a 1.3 Gbit/s SKR over a 10-dB-loss channel. To the best of our knowledge, this is the first QKD demonstration that achieves a gigabit-per-second-class SKR, representing a critical advance toward high-rate QKD at metropolitan-area distances.

quant-ph↗
arXiv2017

Exploiting Occlusion in Non-Line-of-Sight Active Imaging

Active non-line-of-sight imaging systems are of growing interest for diverse applications. The most commonly proposed approaches to date rely on exploiting time-resolved measurements, i.e., measuring the time it takes for short light pulses to transit the scene. This typically requires expensive, specialized, ultrafast lasers and detectors that must be carefully calibrated. We develop an alternative approach that exploits the valuable role that natural occluders in a scene play in enabling accurate and practical image formation in such settings without such hardware complexity. In particular, we demonstrate that the presence of occluders in the hidden scene can obviate the need for collecting time-resolved measurements, and develop an accompanying analysis for such systems and their generalizations. Ultimately, the results suggest the potential to develop increasingly sophisticated future systems that are able to identify and exploit diverse structural features of the environment to reconstruct scenes hidden from view.

eess.IV↗
arXiv2017

Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators

We establish a symmetry-operator framework for designing quantum error correcting~(QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for $χ^{(2)}$-interaction based quantum computation: the $χ^{(2)}$ parity-check code, the $χ^{(2)}$ embedded error-correcting code, and the $χ^{(2)}$ binomial code, all of which detect photon-loss or photon-gain errors by means of photon-number parity measurements and then correct them via $χ^{(2)}$ Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes. The $χ^{(2)}$ binomial code is of special interest because, with $m\le N$ identified from channel monitoring, it can correct $m$-photon loss errors, $m$-photon gain errors, and $(m-1)$th-order dephasing errors using logical qudits that are encoded in $O(N)$ photons. In comparison, other bosonic QEC codes require $O(N^2)$ photons to correct the same degree of bosonic errors. Such improved photon-efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the $χ^{(2)}$ parity-check code and the $χ^{(2)}$ embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our $χ^{(2)}$ QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets.

quant-ph↗
arXiv2017

Quantum illumination for enhanced detection of Rayleigh-fading targets

Quantum illumination (QI) is an entanglement-enhanced sensing system whose performance advantage over a comparable classical system survives its usage in an entanglement-breaking scenario plagued by loss and noise. In particular, QI's error-probability exponent for discriminating between equally-likely hypotheses of target absence or presence is 6 dB higher than that of the optimum classical system using the same transmitted power. This performance advantage, however, presumes that the target return, when present, has known amplitude and phase, a situation that seldom occurs in lidar applications. At lidar wavelengths, most target surfaces are sufficiently rough that their returns are speckled, i.e., they have Rayleigh-distributed amplitudes and uniformly-distributed phases. QI's optical parametric amplifier receiver -- which affords a 3 dB better-than-classical error-probability exponent for a return with known amplitude and phase -- fails to offer any performance gain for Rayleigh-fading targets. We show that the sum-frequency generation receiver [Phys. Rev. Lett. 118, 040801 (2017)] -- whose error-probability exponent for a nonfading target achieves QI's full 6 dB advantage over optimum classical operation -- outperforms the classical system for Rayleigh-fading targets. In this case, QI's advantage is subexponential: its error probability is lower than the classical system's by a factor of $1/\ln(M\barκN_S/N_B)$, when $M\barκN_S/N_B \gg 1$, with $M\gg 1$ being the QI transmitter's time-bandwidth product, $N_S \ll 1$ its brightness, $\barκ$ the target's average reflectivity, and $N_B$ the background light's brightness.

quant-ph↗
arXiv2017

Entanglement-Enhanced Lidars for Simultaneous Range and Velocity Measurements

Lidar is a well known optical technology for measuring a target's range and radial velocity. We describe two lidar systems that use entanglement between transmitted signals and retained idlers to obtain significant quantum enhancements in simultaneous measurement of these parameters. The first entanglement-enhanced lidar circumvents the Arthurs-Kelly uncertainty relation for simultaneous measurement of range and radial velocity from detection of a single photon returned from the target. This performance presumes there is no extraneous (background) light, but is robust to the roundtrip loss incurred by the signal photons. The second entanglement-enhanced lidar---which requires a lossless, noiseless environment---realizes Heisenberg-limited accuracies for both its range and radial-velocity measurements, i.e., their root-mean-square estimation errors are both proportional to $1/M$ when $M$ signal photons are transmitted. These two lidars derive their entanglement-based enhancements from use of a unitary transformation that takes a signal-idler photon pair with frequencies $ω_S$ and $ω_I$ and converts it to a signal-idler photon pair whose frequencies are $(ω_S + ω_I)/2$ and $ω_S-ω_I$. Insight into how this transformation provides its benefits is provided through an analogy to superdense coding.

quant-ph↗