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-mixedstate 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. DOI: 10.1103/PhysRevLett.118.040801 Introduction.-Entanglement is essential for deviceindependent quantum cryptography [1], quantum computing [2], and quantum-enhanced metrology [3]. It has also been employed in frequency and phase estimation to beat their standard quantum limits on measurement precision [4][5][6][7][8][9][10]. Furthermore, entanglement has applications across diverse research areas, including dynamic biological measurement [11], delicate material probing [12], gravitational wave detection [13], and quantum lithography [14]. Entanglement, however, is fragile; it is easily destroyed by quantum decoherence arising from environmental loss and noise. Consequently, the entanglement-enabled performance advantages of most quantum-enhanced sensing schemes quickly dissipate with increasing quantum decoherence, challenging their merits for practical situations.Quantum illumination (QI) is an entanglement-enhanced paradigm for target detection that thrives on entanglementbreaking loss and noise [15][16][17][18][19][20][21][22]. Its optimum quantum receiver enjoys a 6 dB advantage in error-probability exponent over optimum classical sensing using the same transmitted photon number. Remarkably, QI's advantage occurs despite the initial entanglement being completely destroyed.To date, the only in-principle realization of QI's optimum quantum receiver requires a Schur transform on a quantum computer [23], so that its physical implementation is unlikely to occur in the near future. At present, the best known suboptimum QI receivers [20,21]-one of which, the optical parametric amplifier (OPA) receiver, has been

Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations-Gaussian operations combined with feed-forwardare chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non-Gaussian states-states not in the convex hull of Gaussian states-are the necessary resource states for universal quantum computation together with free operations. We introduce a monotone to quantify the genuine non-Gaussianity of resource states, in analogy to the stabilizer theory. A direct application of our resource theory is to bound the conversion rate between genuine non-Gaussian states. Finally, we give a protocol that probabilistically distills genuine non-Gaussianity-increases the genuine non-Gaussianity of resource states-only using free operations and postselection on Gaussian measurements, where our theory gives an upper bound for the distillation rate. In particular, the same protocol allows the distillation of cubic phase states, which enable universal quantum computation when combined with free operations.

The channel loss incurred in long-distance transmission places a significant burden on quantum key distribution (QKD) systems: they must defeat a passive eavesdropper who detects all the light lost in the quantum channel and does so without disturbing the light that reaches the intended destination. The current QKD implementation with the highest long-distance secret-key rate meets this challenge by transmitting no more than one photon per bit [Opt. Express 21, 24550-24565 (2013)]. As a result, it cannot achieve the Gbps secret-key rate needed for one-time pad encryption of large data files unless an impractically large amount of multiplexing is employed. We introduce floodlight QKD (FL-QKD), which floods the quantum channel with a high number of photons per bit distributed over a much greater number of optical modes. FL-QKD offers security against the optimum frequency-domain collective attack by transmitting less than one photon per mode and using photon-coincidence channel monitoring, and it is completely immune to passive eavesdropping. More importantly, FL-QKD is capable of a 2 Gbps secret-key rate over a 50 km fiber link, without any multiplexing, using available equipment, i.e., no new technology need be developed. FL-QKD achieves this extraordinary secret-key rate by virtue of its unprecedented secret-key efficiency, in bits per channel use, which exceeds those of state-of-the-art systems by two orders of magnitude.

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 the 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.

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.

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 the 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.

The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity and gravity. Here, we extend the framework for exploring information scrambling to infinite dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: i) scrambling in the phase space of a single mode and ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct 'types' of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out and quasi scrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed.

Quantum metrology [1-4] enables a measurement sensitivity below the standard quantum limit (SQL), as demonstrated in the Laser Interferometer Gravitational-wave Observatory (LIGO) [5,6]. As a unique quantum resource, entanglement has been utilized to enhance the performance of, e.g., microscopy [7], target detection [8], and phase estimation [9]. To date, almost all existing entanglementenhanced sensing demonstrations are restricted to improving the performance of probing optical parameters at a single sensor, but a multitude of applications rely on an array of sensors that work collectively to undertake sensing tasks in the radiofrequency (RF) and microwave spectral ranges. Here, we propose and experimentally demonstrate a reconfigurable RF-photonic sensor network comprised of three entangled sensor nodes. We show that the entanglement shared by the sensors can be tailored to substantially increase the precision of parameter estimation in networked sensing tasks, such as estimating the angle of arrival (AoA) of an RF field. Our work would open a new avenue toward utilizing quantum metrology for ultrasensitive positioning, navigation, and timing.A variety of sensing scenarios commonly operate in the RF and microwave spectral ranges, rather than at the optical wavelengths like LIGO, thus requiring a different mechanism to achieve a quantum enhancement. In this regard, quantum illumination enables a signal-to-noise ratio (SNR) advantage over classical schemes in the RF and microwave where ambient noise is abundant [8,[10][11][12][13][14], but quantum illumination's operational range and quantum enhancement are limited by large diffraction in the microwave and a lack of efficient quantum memories.Recent advances in RF and microwave photonics [15] offer new insights for sensing. In RF-photonic sensing, RF signals are carried over to the optical domain by * zsz@email.arizona.edu † Equal contributions