Entanglement-enhanced sensing in a lossy and noisy environment

The second-order coherence analysis of number state propagation through dispersive non-Hermitian multilayered structures

To examine the second-order coherence of light propagation of quantum states in arbitrary directions through dispersive non-Hermitian optical media, we considered two sets of non-Hermitian periodic structures that consist of gain/loss unit cells. We show that each batch can satisfy the parity-time symmetry conditions at a distinct frequency. We then varied the gain/loss strength in the stable electromagnetic regime to evaluate the transmittance of N-photon number states through each structure. The results show both sets preserve their antibunching characteristics under specific incident light conditions. Furthermore, s(p)-polarized light exhibits higher (lower) second-order coherence at larger incident angles. In addition, the antibunching features of the transmitted states degrade with an increase in the number of unit cells in multilayered structures for both polarizations.

Observing thermal lensing with quantum light

The introduction of quantum methods in spectroscopy can provide enhanced performance and technical advantages in the management of noise. We investigate the application of quantum illumination in a pump and probe experiment. Thermal lensing in a suspension of gold nanorods is explored using a classical beam as the pump and the emission from parametric downconversion as the probe. We obtain an insightful description of the behavior of the suspension under pumping with a method known to provide good noise rejection. Our findings are a further step toward investigating the effects of quantum light in complex plasmonic media.

Demonstration of quantum-enhanced rangefinding robust against classical jamming

We demonstrate a quantum-enhanced lidar capable of performing confident target detection and rangefinding in the presence of strong, time-varying classical noise whilst operating with over five orders of magnitude separation between signal and background levels and target reflectivities down to -52 dB. We use a log-likelihood-based framework to introduce a new protocol for dynamic background tracking, verifying resilience of our system to both fast- and slow-modulation jamming in regimes where a classical illumination-based system fails to find a target. These results demonstrate the advantage of exploiting quantum correlations for lidar applications, providing a clear route to implementation in real-world scenarios.

Multi-field-driven optomechanical entanglement

Cavity optomechanical (COM) entanglement, playing an essential role in building quantum networks and enhancing quantum sensors, is usually weak and easily destroyed by noises. As feasible and effective ways to overcome this obstacle, optical or mechanical parametric modulations have been used to improve the quality of quantum squeezing or entanglement in various COM systems. However, the possibility of combining these powerful means to enhance COM entanglement has yet to be explored. Here, we fill this gap by studying a COM system containing an intra-cavity optical parametric amplifier (OPA), driven optically and mechanically. By tuning the relative strength and the frequency mismatch of optical and mechanical driving fields, we find that constructive interference can emerge and significantly improve the strength of COM entanglement and its robustness to thermal noises. This work sheds what we believe to be a new light on preparing and protecting quantum states with multi-field driven COM systems for diverse applications.

Optimized receiver design for entanglement-assisted communication using BPSK

The use of pre-shared entanglement in entanglement-assisted communication offers a superior alternative to classical communication, especially in the photon-starved regime and highly noisy environments. In this paper, we analyze the performance of several low-complexity receivers that use optical parametric amplifiers. The simulations demonstrate that receivers employing an entanglement-assisted scheme with phase-shift-keying modulation can outperform classical capacities. We present a 2x2 optical hybrid receiver for entanglement-assisted communication and show that it has a roughly 10% lower error probability compared to previously proposed optical parametric amplifier-based receivers for more than 10 modes. However, the capacity of the optical parametric amplifier-based receiver exceeds the Holevo capacity and the capacities of the optical phase conjugate receiver and 2x2 optical hybrid receiver in the case of a single mode. The numerical findings indicate that surpassing the Holevo and Homodyne capacities does not require a large number of signal-idler modes. Furthermore, we find that using unequal priors for BPSK provides roughly three times the information rate advantage over equal priors.

Bound for Gaussian-state quantum illumination using a direct photon measurement

It is important to find feasible measurement bounds for quantum information protocols. We present analytic bounds for quantum illumination with Gaussian states when using an on-off detection or a photon number resolving (PNR) detection, where its performance is evaluated with signal-to-noise ratio. First, for coincidence counting measurement, the best performance is given by the two-mode squeezed vacuum (TMSV) state which outperforms the coherent state and the classically correlated thermal (CCT) state. However, the coherent state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Second, the performance is enhanced by taking Fisher information approach with all counting probabilities including non-detection events. In the Fisher information approach, the TMSV state still presents the best performance but the CCT state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Furthermore, we show that it is useful to take the PNR detection on the signal mode and the on-off detection on the idler mode, which reaches similar performance of using PNR detection on both modes.

Evaluation on quantum illumination radar with quantum limited amplification

Based on Quantum illumination (QI) protocol, researcshers have developed prototypes of quantum radar and demonstrated its quantum enhancement. Nevertheless, there are still difficulties in the practical application for QI radar, especially the trade-off between the detection range and quantum enhancement, as well as the construction of the optimized receiver. Some studies have suggested that the potential solutions to these difficulties are to deploy the quantum limited amplifiers in QI radars, and have envisioned different amplification schemes. In this paper, we establish a universal and effective method to evaluate the signal-to-noise ratio of QI radar. It connects QI radar theory with classical radar signal processing theory, providing support for researchers to evaluate the performance of various QI radar schemes from a radar perspective. Based on this method, we prove that any quantum limited phase-insensitive amplification scheme will seriously weaken the quantum enhancement of QI radar. Furthermore, we also demonstrate that the QI radar with phase-sensitive amplified idler has no advantage over the optimal classical illumination. These results can help us avoid some unreasonable QI radar schemes. In addition, we believe that the proposed method can also be applied to explore other potential QI radar schemes and contribute to promoting the application development of QI radar.

Quantum illumination using polarization-path entangled single photons for low reflectivity object detection in a noisy background

Detecting object with low reflectivity embedded within a noisy background is a challenging task. Quantum correlations between pairs of quantum states of light, though are highly sensitive to background noise and losses, offer advantages over traditional illumination methods. Instead of using correlated photon pairs which are sensitive, we experimentally demonstrate the advantage of using heralded single-photons entangled in polarization and path degree of freedom for quantum illumination. In the study, the object of different reflectivity is placed along the path of the signal in a variable thermal background before taking the joint measurements and calculating the quantum correlations. We show the significant advantage of using non-interferometric measurements along the multiple paths for single photon to isolate the signal from the background noise and outperform in detecting and ranging the low reflectivity objects even when the signal-to-noise ratio is as low as 0.03. Decrease in visibility of polarization along the signal path also results in similar observations. This will have direct relevance to the development of single-photon based quantum LiDAR and quantum imaging.

Compact all-fiber quantum-inspired LiDAR with over 100 dB noise rejection and single photon sensitivity

Entanglement and correlation of quantum light can enhance LiDAR sensitivity in the presence of strong background noise. However, the power of such quantum sources is fundamentally limited to a stream of single photons and cannot compete with the detection range of high-power classical LiDAR transmitters. To circumvent this, we develop and demonstrate a quantum-inspired LiDAR prototype based on coherent measurement of classical time-frequency correlation. This system uses a high-power classical source and maintains the high noise rejection advantage of quantum LiDARs. In particular, we show that it can achieve over 100dB rejection (with 100ms integration time) of indistinguishable (with statistically identical properties in every degree of freedom) in-band noise while still being sensitive to single photon signals. In addition to the LiDAR demonstration, we also discuss the potential of the proposed LiDAR receiver for quantum information applications. In particular, we propose the chaotic quantum frequency conversion technique for coherent manipulation of high dimensional quantum states of light. It is shown that this technique can provide improved performance in terms of selectivity and efficiency as compared to pulse-based quantum frequency conversion.

Quantum Induced Coherence Light Detection and Ranging

Quantum illumination has been proposed and demonstrated to improve the signal-to-noise ratio (SNR) in light detection and ranging (LiDAR). When relying on coincidence detection alone, such a quantum LiDAR is limited by the timing jitter of the detector and suffers from jamming noise. Inspired by the Zou-Wang-Mandel experiment, we design, construct, and validate a quantum induced coherence (QuIC) LiDAR which is inherently immune to ambient and jamming noises. In traditional LiDAR the direct detection of the reflected probe photons suffers from deteriorating SNR for increasing background noise. In QuIC LiDAR we circumvent this obstacle by only detecting the entangled reference photons, whose single-photon interference fringes are used to obtain the distance of the object, while the reflected probe photons are used to erase path information of the reference photons. In consequence, the noise accompanying the reflected probe light has no effect on the detected signal. We demonstrate such noise resilience with both LED and laser light to mimic the background and jamming noise. The proposed method paves a new way of battling noise in precise quantum electromagnetic sensing and ranging.

Sensitive enhancement of cat state quantum illumination

Quantum illumination is a binary hypothesis testing to detect a possible low-reflective object. Theoretically, both cat state illumination and Gaussian-state illumination possess the upper bound of 3dB sensitivity gain, over the usual coherent state illumination, for the significantly low illuminating intensity. Here, we investigate further how to enhance the quantum advantage of quantum illumination by optimizing the illuminating cat states for larger illuminating intensity. By comparing the quantum Fisher information or error exponent, we show that the sensitivity of the quantum illumination with generic cat states proposed here can be optimized further, and the 10.3% sensitive enhancement over the previous cat state illumination can be obtained.

High-fidelity quantum information transmission using a room-temperature nonrefrigerated lossy microwave waveguide

Quantum microwave transmission is key to realizing modular superconducting quantum computers and distributed quantum networks. A large number of incoherent photons are thermally generated within the microwave frequency spectrum. The closeness of the transmitted quantum state to the source-generated quantum state at the input of the transmission link (measured by the transmission fidelity) degrades due to the presence of the incoherent photons. Hence, high-fidelity quantum microwave transmission has long been considered to be infeasible without refrigeration. In this study, we propose a novel method for high-fidelity quantum microwave transmission using a room-temperature lossy waveguide. The proposed scheme consists of connecting two cryogenic nodes (i.e., a transmitter and a receiver) by the room-temperature lossy microwave waveguide. First, cryogenic preamplification is implemented prior to transmission. Second, at the receiver side, a cryogenic loop antenna is placed inside the output port of the waveguide and coupled to an LC harmonic oscillator located outside the waveguide. The loop antenna converts quantum microwave fields to a quantum voltage across the coupled LC harmonic oscillator. Noise photons are induced across the LC oscillator including the source generated noise, the preamplification noise, the thermal occupation of the waveguide, and the fluctuation-dissipation noise. The loop antenna detector at the receiver is designed to extensively suppress the induced photons across the LC oscillator. The signal transmittance is maintained intact by providing significant preamplification gain. Our calculations show that high-fidelity quantum transmission (i.e., more than [Formula: see text]) is realized based on the proposed scheme for transmission distances reaching 100 m.

Comparison of SNR gain between quantum illumination radar and classical radar

It has been proved that quantum illumination (QI) radar has the quantum advantages in error-probability exponent. However, the error-probability exponent is not a recognized figure of merit in the radar literature, nor does it correspond in a straightforward manner to any such figure of merit. Signal to noise ratio (SNR) gain is an important criterion in radar theory. While, the theoretical analysis of quantum enhancement in SNR gain of QI radar has not been reported. In this paper, we compare the physical fundamental of matched filter (MF), which can achieve the optimal SNR gain under white noise in classical radar theory, and phase conjugation (PC) receiver. Furthermore, the quantum enhancement of SNR gain in QI radar is studied. It is shown that QI radar with practical receivers can achieve about 3dB quantum advantage in SNR gain. In addition, in the case of extremely weak signal, it can potentially achieve tens of dB enhancement in SNR gain compared with the MF based classical radar.

Quantum and non-local effects offer over 40 dB noise resilience advantage towards quantum lidar

Non-local effects have the potential to radically move forward quantum enhanced imaging to provide an advantage over classical imaging not only in laboratory environments but practical implementation. In this work, we demonstrate a 43dB higher signal-to-noise ratio (SNR) using a quantum enhanced LiDAR based on time-frequency entanglement compared with a classical phase-insensitive quantum imaging system. Our system can tolerate more than 3 orders of magnitude higher noise than classical single-photon counting quantum imaging systems before detector saturation with a detector dead time of 25ns. To achieve these advantages, we use non-local cancellation of dispersion to take advantage of the strong temporal correlations in photon pairs in spite of the orders of magnitude larger detector temporal uncertainty. We go on to incorporate this scheme with purpose-built scanning collection optics to image non-reflecting targets in an environment with noise.

Sensitivity to noise is currently an obstacle to the use of quantum imaging techniques in real-world scenarios. Here, exploiting non-local cancellation of dispersion on time-frequency entangled photons, the authors show a 43dB improvement in resilience to noise for imaging protocols towards a quantum LiDAR.

On Entanglement-Assisted Multistatic Radar Techniques

Entanglement-based quantum sensors have much better sensitivity than corresponding classical sensors in a noisy and lossy regime. In our recent paper, we showed that the entanglement-assisted (EA) joint monostatic–bistatic quantum radar performs much better than conventional radars. Here, we propose an entanglement-assisted (EA) multistatic radar that significantly outperforms EA bistatic, coherent state-based quantum, and classical radars. The proposed EA multistatic radar employs multiple entangled transmitters performing transmit-side optical phase conjugation, multiple coherent detection-based receivers serving as EA detectors, and a joint detector.

Demonstration of Entanglement-Enhanced Covert Sensing

The laws of quantum physics endow superior performance and security for information processing: quantum sensing harnesses nonclassical resources to enable measurement precision unmatched by classical sensing, whereas quantum cryptography aims to unconditionally protect the secrecy of the processed information. Here, we present the theory and experiment for entanglement-enhanced covert sensing, a paradigm that simultaneously offers high measurement precision and data integrity by concealing the probe signal in an ambient noise background so that the execution of the protocol is undetectable with a high probability. We show that entanglement offers a performance boost in estimating the imparted phase by a probed object, as compared to a classical protocol at the same covertness level. The implemented entanglement-enhanced covert sensing protocol operates close to the fundamental quantum limit by virtue of its near-optimum entanglement source and quantum receiver. Our work is expected to create ample opportunities for quantum information processing at unprecedented security and performance levels.

Entanglement-Assisted Joint Monostatic-Bistatic Radars

With the help of entanglement, we can build quantum sensors with sensitivity better than that of classical sensors. In this paper we propose an entanglement assisted (EA) joint monostatic-bistatic quantum radar scheme, which significantly outperforms corresponding conventional radars. The proposed joint monostatic-bistatic quantum radar is composed of two radars, one having both wideband entangled source and EA detector, and the second one with only an EA detector. The optical phase conjugation (OPC) is applied on the transmitter side, while classical coherent detection schemes are applied in both receivers. The joint monostatic-bistatic integrated EA transmitter is proposed suitable for implementation in LiNbO₃ technology. The detection probability of the proposed EA joint target detection scheme outperforms significantly corresponding classical, coherent states-based quantum detection, and EA monostatic detection schemes. The proposed EA joint target detection scheme is evaluated by modelling the direct radar return and forward scattering channels as both lossy and noisy Bosonic channels, and assuming that the distribution of entanglement over idler channels is not perfect.

Correlation Technologies for Emerging Wireless Applications

In this article, we introduce correlation technologies both at RF/mmWave and baseband frequencies. At RF and mmWave frequencies, power-spectra and energy-spectra metrics are introduced for measuring the power-density of mobile devices and systems. New ASIC-embedded smart connectors are developed for bringing correlation-based signal processing close to antenna modules. At baseband frequencies, DSP-based convolutional accelerators are proposed for fast and accurate measurement of EVM (error vector magnitude) using correlation technologies. Porting of the DSP-based convolutional accelerators into advanced fully depleted silicon-on-insulator (FDSOI)-based ASIC platforms for co-integration with adaptive RF/mmWave front-end modules will enable real-time extraction of auto-correlation and cross-correlation functions of stochastic signals. Perspectives for optically synchronized interferometric-correlation technologies are drawn for accurate measurements in noisy environments of stochastic EM fields using power-spectra and energy-spectra metrics. Adoption of correlation technologies will foster new paradigms relative to interactions of humans with smart devices and systems in randomly fluctuating environments. The resulting new paradigms will open new possibilities in communication theory for properly combining and reconciling information signal theory (Shannon information-based entropy) and physical information theory (statistical-physics-based entropy) into a unified framework.

Propagation of temporal mode multiplexed optical fields in fibers: influence of dispersion

Exploiting two interfering fields which are initially in the same temporal mode but with the spectra altered by propagating through different fibers, we characterize how the spectral profiles of temporal modes change with the fiber induced dispersion by measuring the fourth-order interference when the order number and bandwidth of temporal modes are varied. The experiment is done by launching a pulsed field in different temporal modes into an unbalanced Mach-Zehnder interferometer, in which the fiber lengths in two arms are different. The results show that the mode mismatch of two interfering fields, reflected by the visibility and pattern of interference, is not only dependent upon the amount of unbalanced dispersion but also related to the order number of temporal mode. In particular, the two interfering fields may become orthogonal under a modest amount of unbalanced dispersion when the mode number of the fields is k ≥ 2. Moreover, we discuss how to recover the spectrally distorted temporal mode by measuring and compensating the transmission induced dispersion. Our investigation paves the way for further investigating the distribution of temporally multiplexed quantum states in fiber network.

Quantum conformance test

We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end products it produces, which is generated according to a given probability distribution. We formulate the problem in the context of hypothesis testing and consider the specific case in which the objects can be modeled as pure loss channels. We demonstrate theoretically that a simple quantum strategy, using readily available resources and measurement schemes in the form of two-mode squeezed vacuum and photon counting, can outperform any classical strategy. We experimentally implement this protocol, exploiting optical twin beams, validating our theoretical results, and demonstrating that, in this task, there is a quantum advantage in a realistic setting.

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.

Experimental Quantum Target Detection Approaching the Fundamental Helstrom Limit

Quantum target detection is an emerging application that utilizes entanglement to enhance the sensing of the presence of an object. Although several experimental demonstrations for certain situations have been reported recently, the single-shot detection limit imposed by the Helstrom limit has not been reached because of the unknown optimum measurements. Here we report an experimental demonstration of quantum target detection, also known as quantum illumination, in the single-photon limit. In our experiment, one photon of the maximally entangled photon pair is employed as the probe signal and the corresponding optimum measurement is implemented at the receiver. We explore the detection problem in different regions of the parameter space and verify that the quantum advantage exists even in a forbidden region of the conventional illumination, where all classical schemes become useless. Our results indicate that quantum illumination breaks the classical limit for up to 40%, while approaching the quantum limit imposed by the Helstrom limit. These results not only demonstrate the advantage of quantum illumination, but also manifest its valuable potential of target detection.

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.

Quantum Ranging with Gaussian Entanglement

It is well known that entanglement can benefit quantum information processing tasks. Quantum illumination, when first proposed, was surprising as the entanglement's benefit survived entanglement-breaking noise. Since then, many efforts have been devoted to study quantum sensing in noisy scenarios. The applicability of such schemes, however, is limited to a binary quantum hypothesis testing scenario. In terms of target detection, such schemes interrogate a single spatiotemporal resolution bin at a time, limiting the impact to radar detection. We resolve this binary-hypothesis limitation by proposing an entanglement-assisted quantum ranging protocol. By formulating a ranging task as a multiary hypothesis testing problem, we show that entanglement enables a 6-dB advantage in the error exponent against the optimal classical scheme. Moreover, the proposed ranging protocol can also be used to implement a pulse-position modulated entanglement-assisted communication protocol. Our ranging protocol reveals entanglement's potential in general quantum hypothesis testing tasks and paves the way toward a quantum-ranging radar with a provable quantum advantage.

A Molecular Approach to Quantum Sensing

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

Entangled photon-pair sources based on three-wave mixing in bulk crystals

Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.

Quantum Plasmonic Sensors

The extraordinary sensitivity of plasmonic sensors is well-known in the optics and photonics community. These sensors exploit simultaneously the enhancement and the localization of electromagnetic fields close to the interface between a metal and a dielectric. This enables, for example, the design of integrated biochemical sensors at scales far below the diffraction limit. Despite their practical realization and successful commercialization, the sensitivity and associated precision of plasmonic sensors are starting to reach their fundamental classical limit given by quantum fluctuations of light-known as the shot-noise limit. To improve the sensing performance of these sensors beyond the classical limit, quantum resources are increasingly being employed. This area of research has become known as "quantum plasmonic sensing", and it has experienced substantial activity in recent years for applications in chemical and biological sensing. This review aims to cover both plasmonic and quantum techniques for sensing, and it shows how they have been merged to enhance the performance of plasmonic sensors beyond traditional methods. We discuss the general framework developed for quantum plasmonic sensing in recent years, covering the basic theory behind the advancements made, and describe the important works that made these advancements. We also describe several key works in detail, highlighting their motivation, the working principles behind them, and their future impact. The intention of the review is to set a foundation for a burgeoning field of research that is currently being explored out of intellectual curiosity and for a wide range of practical applications in biochemistry, medicine, and pharmaceutical research.

Gaussian state-based quantum illumination with simple photodetection

Proofs of the quantum advantage available in imaging or detecting objects under quantum illumination can rely on optimal measurements without specifying what they are. We use the continuous-variable Gaussian quantum information formalism to show that quantum illumination is better for object detection compared with coherent states of the same mean photon number, even for simple direct photodetection. The advantage persists if signal energy and object reflectivity are low and background thermal noise is high. The advantage is even greater if we match signal beam detection probabilities rather than mean photon number. We perform all calculations with thermal states, even for non-Gaussian conditioned states with negative Wigner functions. We simulate repeated detection using a Monte-Carlo process that clearly shows the advantages obtainable.

Quantum rangefinding

Quantum light generated in non-degenerate squeezers has many applications such as sub-shot-noise transmission measurements to maximise the information extracted by one photon or quantum illumination to increase the probability in target detection. However, any application thus far fails to consider the thermal characteristics of one half of the bipartite down-converted photon state often used in these experiments. We show here that a maximally mixed state, normally viewed as nuisance, can indeed be used to extract information about the position of an object while at the same time providing efficient camouflaging against other thermal or background light.

Entanglement-Assisted Absorption Spectroscopy

Spectroscopy is an important tool for probing the properties of materials, chemicals, and biological samples. We design a practical transmitter-receiver system that exploits entanglement to achieve a provable quantum advantage over all spectroscopic schemes based on classical sources. To probe the absorption spectra, modeled as a pattern of transmissivities among different frequency modes, we employ broadband signal-idler pairs in two-mode squeezed vacuum states. At the receiver side, we apply photodetection after optical parametric amplification. Finally, we perform a maximum likelihood decision test on the measurement results, achieving an error probability orders of magnitude lower than the optimum classical systems in various examples, including "wine tasting" and "drug testing" where real molecules are considered. In detecting the presence of an absorption line, our quantum scheme achieves the optimum performance allowed by quantum mechanics. The quantum advantage in our system is robust against noise and loss, which makes near-term experimental demonstration possible.

Ultimate Limits for Multiple Quantum Channel Discrimination

Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication. Although the limits of hypothesis testing between quantum states have been completely clarified by the pioneering works of Helstrom in the 1970s, the more difficult problem of hypothesis testing with quantum channels, i.e., channel discrimination, is less understood. This is mainly due to the complications coming from the use of input entanglement and the possibility of employing adaptive strategies. In this Letter, we establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels. We also show that this lower bound is achievable when the channels have certain symmetries. As an example, we apply our results to the problem of channel position finding, where the goal is to identify the location of a target channel among multiple background channels. In this general setting, we find that the use of entanglement offers a great advantage over strategies without entanglement, with nontrivial implications for data readout, target detection, and quantum spectroscopy.

Microwave quantum illumination using a digital receiver

Quantum illumination uses entangled signal-idler photon pairs to boost the detection efficiency of low-reflectivity objects in environments with bright thermal noise. Its advantage is particularly evident at low signal powers, a promising feature for applications such as noninvasive biomedical scanning or low-power short-range radar. Here, we experimentally investigate the concept of quantum illumination at microwave frequencies. We generate entangled fields to illuminate a room-temperature object at a distance of 1 m in a free-space detection setup. We implement a digital phase-conjugate receiver based on linear quadrature measurements that outperforms a symmetric classical noise radar in the same conditions, despite the entanglement-breaking signal path. Starting from experimental data, we also simulate the case of perfect idler photon number detection, which results in a quantum advantage compared with the relative classical benchmark. Our results highlight the opportunities and challenges in the way toward a first room-temperature application of microwave quantum circuits.

Demonstration of a Reconfigurable Entangled Radio-Frequency Photonic Sensor Network

Quantum metrology takes advantage of nonclassical resources such as entanglement to achieve a sensitivity level below the standard quantum limit. To date, almost all quantum-metrology demonstrations are restricted to improving the measurement performance at a single sensor, but a plethora of applications require multiple sensors that work jointly to tackle distributed sensing problems. Here, we propose and experimentally demonstrate a reconfigurable sensor network empowered by continuous-variable (CV) multipartite entanglement. Our experiment establishes a connection between the entanglement structure and the achievable quantum advantage in different distributed sensing problems. The demonstrated entangled sensor network is composed of three sensor nodes each equipped with an electro-optic transducer for the detection of radio-frequency (RF) signals. By properly tailoring the CV multipartite entangled states, the entangled sensor network can be reconfigured to maximize the quantum advantage in distributed RF sensing problems such as measuring the angle of arrival of an RF field. The rich physics of CV multipartite entanglement unveiled by our work would open a new avenue for distributed quantum sensing and would lead to applications in ultrasensitive positioning, navigation, and timing.

Quantum noise radar: superresolution with quantum antennas by accessing spatiotemporal correlations

We suggest overcoming the "Rayleigh catastrophe" and reaching superresolution for imaging with both spatially and temporally correlated field of a superradiant quantum antenna. Considering far-field radiation of two interacting spontaneously emitting two-level systems, we show that for the measurement of the temporally delayed second-order correlation function of the scattered field, the Fisher information does not tend to zero with diminishing the distance between a pair of scatterers even for non-sharp time-averaged detection. For position estimation of more scatterers, the measurement of the time-delayed function is able to provide a considerable accuracy gain over the zero-delayed function. We also show that the superresolution with the considered quantum antenna can be achieved for both near-field imaging and for estimating the antenna parameters.

Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams

Loss measurements are at the base of spectroscopy and imaging, thus permeating all the branches of science, from chemistry and biology to physics and material science. However, quantum mechanics laws set the ultimate limit to the sensitivity, constrained by the probe mean energy. This can be the main source of uncertainty, for example when dealing with delicate systems such as biological samples or photosensitive chemicals. It turns out that ordinary (classical) probe beams, namely with Poissonian photon number distribution, are fundamentally inadequate to measure small losses with the highest sensitivity. It is known that quantum-correlated pair of beams, named “twin-beam state”, allows surpassing this classical limit. Here we demonstrate they can reach the ultimate sensitivity for all energy regimes (even less than one photon per mode) with the simplest measurement strategy. One beam of the pair addresses the sample, while the second one is used as a reference to compensate both for classical drifts and for fluctuation at the most fundamental quantum level. This capability of selfcompensating for unavoidable instability of the sources and detectors allows also to strongly reduce the bias in practical measurement. Moreover, we report the best sensitivity per photon ever achieved in loss estimation experiments.

Finite-time quantum entanglement in propagating squeezed microwaves

Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of non-commuting observables between two subsystems. At the same time, these subsystems themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental dephasing process of quantum cross-correlations in continuous-variable propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain the insight into finite-time entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.

Gaussian Hypothesis Testing and Quantum Illumination

Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.

Quantum illumination reveals phase-shift inducing cloaking

In quantum illumination entangled light is employed to enhance the detection accuracy of an object when compared with the best classical protocol. On the other hand, cloaking is a stealth technology based on covering a target with a material deflecting the light around the object to avoid its detection. Here, we propose a quantum illumination protocol especially adapted to quantum microwave technology. This protocol seizes the phase-shift induced by some cloaking techniques, such as scattering reduction, allowing for a 3 dB improvement in the detection of a cloaked target. The method can also be employed for the detection of a phase-shift in bright environments in different frequency regimes. Finally, we study the minimal efficiency required by the photocounter for which the quantum illumination protocol still shows a gain with respect to the classical protocol.

Quantum Estimation Methods for Quantum Illumination

Quantum illumination consists in shining quantum light on a target region immersed in a bright thermal bath with the aim of detecting the presence of a possible low-reflective object. If the signal is entangled with the receiver, then a suitable choice of the measurement offers a gain with respect to the optimal classical protocol employing coherent states. Here, we tackle this detection problem by using quantum estimation techniques to measure the reflectivity parameter of the object, showing an enhancement in the signal-to-noise ratio up to 3 dB with respect to the classical case when implementing only local measurements. Our approach employs the quantum Fisher information to provide an upper bound for the error probability, supplies the concrete estimator saturating the bound, and extends the quantum illumination protocol to non-Gaussian states. As an example, we show how Schrödinger's cat states may be used for quantum illumination.

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.