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Abstract Advances in satellite quantum communications aim at reshaping the global telecommunication network by increasing the security of the transferred information. Here, we study the effects of atmospheric turbulence in continuous-variable entanglement distribution and quantum teleportation in the optical regime between a ground station and a satellite. More specifically, we study the degradation of entanglement due to various error sources in the distribution, namely, diffraction, atmospheric attenuation, turbulence, and detector inefficiency, in both downlink and uplink scenarios. As the fidelity of a quantum teleportation protocol using these distributed entangled resources is not sufficient, we include an intermediate station for either state generation, or beam refocusing, in order to reduce the effects of atmospheric turbulence and diffraction, respectively. The results show the feasibility of free-space entanglement distribution and quantum teleportation in downlink paths up to the LEO region, but also in uplink paths with the help of the intermediate station. Finally, we complete the study with microwave-optical comparison in bad weather situations, and with the study of horizontal paths in ground-to-ground and inter-satellite quantum communication.

Abstract We provide a rigorous security proof of continuous-variable measurement-device-independent quantum key distribution which incorporates finite-size effects and composable terms. In order to use realistic and optimized parameters and be able to derive results close to experimental expectations, we run protocol simulations supported by a Python library, including all the protocol operations, from simulating the quantum communication till the extraction of the final key.

With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks. Millimeter (mm)-waves and terahertz (THz) with high carrier frequencies are proposed as the enabling technologies to overcome Shannon's channel capacity limit of existing communication systems by providing ultrawide bandwidth signals. Mm-waves and THz are also able to build wireless links compatible with optical communication systems. However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100 GHz–10 THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems. Here, we show that secure mm-waves and THz quantum key distribution (QKD) can be achieved when the sources and detectors operate at cryogenic temperatures down to T = 4 K. We compare single-input single-output and multiple-input multiple-output (MIMO) continuous variable THz quantum key distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges between f = 100 GHz and 1 THz. Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secret communication distance of more than 5 km at f = 100 GHz and T = 4 K by using 1024 × 1024 antennas. Our results for the first time show the possibility of mm-waves and THz MIMO CVQKD with the system operating at temperatures below T = 50 K, which may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from intersatellite and deep space to indoor and short-distance communications.

Abstract A continuous variable (CV), measurement device independent (MDI) quantum key distribution (QKD) protocol is analyzed, enabling three parties to connect for quantum conferencing. We utilise a generalised Bell detection at an untrusted relay and a postselection procedure, in which distant parties reconcile on the signs of the displacements of the quadratures of their prepared coherent states. We derive the rate of the protocol under a collective pure-loss attack, demonstrating improved rate-distance performance compared to the equivalent non-post-selected protocol. In the symmetric configuration in which all the parties lie the same distance from the relay, we find a positive key rate over 6 km. Such postselection techniques can be used to improve the rate of multi-party quantum conferencing protocols at longer distances at the cost of reduced performance at shorter distances.

We discuss the limitations imposed on entanglement distribution, quantum teleportation, and quantum communication by holographic bounds, such as the Bekenstein bound and Susskind's spherical entropy bound. For continuous-variable (CV) quantum information, we show how the naïve application of holographic corrections disrupts well-established results. These corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised Pirandola-Laurenza-Ottaviani-Banchi bound for quantum communication. While these mathematical corrections do not immediately impact practical quantum technologies, they are critical for a deeper theoretical understanding of quantum information theory.

Abstract Gaussian networks are fundamental objects in network information theory. Here many senders and receivers are connected by physically motivated Gaussian channels, while auxiliary Gaussian components, such as Gaussian relays, are entailed. Whilst the theoretical backbone of classical Gaussian networks is well established, the quantum analog is yet immature. Here, we theoretically tackle composable security of arbitrary Gaussian quantum networks, with generally untrusted nodes, in the finite-size regime. We put forward a general methodology for parameter estimation, which is only based on the data shared by the remote end-users. Taking a chain of identical quantum links as an example, we further demonstrate our study. Additionally, we find that the key rate of a quantum amplifier-assisted chain can ideally beat the fundamental repeaterless limit with practical block sizes. However, this objective is practically questioned leading the way to future network/chain designs.

Continuous-variable QKD protocols are usually easier to implement than discrete-variables ones, but their security analyses are less developed. Here, the authors propose and demonstrate in the lab a CVQKD protocol that can generate composable keys secure against collective attacks.

Abstract Due to the difficulties of implementing joint measurements, quantum illumination schemes that are based on signal‐idler entanglement are difficult to implement in practice. For this reason, one may consider quantum‐inspired designs of quantum lidar/radar where the input sources are semi‐classical (coherent states) while retaining the quantum aspects of the detection. The performance of these designs could be studied in the context of asymmetric hypothesis testing by resorting to the quantum Stein’s lemma. However, here the authors discuss that, for typical finite‐size regimes, the second‐ and third‐order expansions associated with this approach are not sufficient to prove quantum advantage.

The security of prepare-and-measure satellite-based quantum key distribution (QKD), under restricted eavesdropping scenarios, is addressed. We particularly consider cases where the eavesdropper, Eve, has limited access to the transmitted signal by Alice and/or Bob’s receiver station. This restriction is modeled by lossy channels between relevant parties, where the transmissivity of such channels can, in principle, be bounded by monitoring techniques. An artifact of such lossy channels is the possibility of having bypass channels, those that are not accessible to Eve but that may not necessarily be characterized by the users either. This creates interesting unexplored scenarios for analyzing QKD security. In this paper, we obtain generic bounds on the key rate in the presence of bypass channels and apply them to continuous-variable QKD protocols with Gaussian encoding with direct and reverse reconciliation. We find regimes of operation in which the above restrictions on Eve can considerably improve system performance. We also develop customized bounds for several protocols in the BB84 family and show that, in certain regimes, even the simple protocol of BB84 with weak coherent pulses is able to offer positive key rates at high channel losses, which would otherwise be impossible under an unrestricted Eve. In this case, the limitation on Eve would allow Alice to send signals with larger intensities than the optimal value under an ideal Eve, which effectively reduces the effective channel loss. In all these cases, the part of the transmitted signal that does not reach Eve can play a nontrivial role in specifying the achievable key rate. Our work opens up new security frameworks for spaceborne quantum communications systems.

As quantum communication networks mature and expand to global scale, free-space links will become increasingly important in bridging the distances involved. The authors provide a model for such links under conditions in which atmospheric turbulence is significant, showing that a finite key rate is possible even in challenging scenarios such as satellite operating at high zenith angle.

Abstract Quantum illumination theoretically promises up to a 6 dB error‐exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime that includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well‐known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally used, and only applicable in the optical domain. This work outlines what is the true classical benchmark for the microwave Quantum illumination using coherent states, providing new bounds on error probability and closed formulae for the receiver operating characteristic, for both optimal (based on quantum relative entropy) and homodyne detection schemes. An alternative source generation procedure based on coherent states is also proposed, which demonstrates the potential to make classically optimal performances achievable in optical applications. The same bounds and measures for the performance of such a source are provided, and its potential utility in the future of room temperature quantum detection schemes in the microwave is discussed.

Abstract Concerted efforts are underway to establish an infrastructure for a global quantum Internet to realise a spectrum of quantum technologies. This will enable more precise sensors, secure communications, and faster data processing. Quantum communications are a front‐runner with quantum networks already implemented in several metropolitan areas. A number of recent proposals have modelled the use of space segments to overcome range limitations of purely terrestrial networks. Rapid progress in the design of quantum devices have enabled their deployment in space for in‐orbit demonstrations. We review developments in this emerging area of space‐based quantum technologies and provide a roadmap of key milestones towards a complete, global quantum networked landscape. Small satellites hold increasing promise to provide a cost effective coverage required to realise the quantum Internet. The state of art in small satellite missions is reviewed and the most current in‐field demonstrations of quantum cryptography are collated. The important challenges in space quantum technologies that must be overcome and recent efforts to mitigate their effects are summarised. A perspective on future developments that would improve the performance of space quantum communications is included. The authors conclude with a discussion on fundamental physics experiments that could take advantage of a global, space‐based quantum network.

Abstract The characterisation of Quantum Channel Discrimination (QCD) offers critical insight for future quantum technologies in quantum metrology, sensing and communications. The task of multi-channel discrimination creates a scenario in which the discrimination of multiple quantum channels can be equated to the idea of pattern recognition, highly relevant to the tasks of quantum reading, illumination and more. Although the optimal quantum strategy for many scenarios is an entangled idler-assisted protocol, the extension to a multi-hypothesis setting invites the exploration of discrimination strategies based on unassisted, multipartite probe states. In this work, we expand the space of possible quantum-enhanced protocols by formulating general classes of unassisted multi-channel discrimination protocols which are not assisted by idler modes. Developing a general framework for idler-free protocols, we perform an explicit investigation in the bosonic setting, studying prominent Gaussian channel discrimination problems for real-world applications. Our findings uncover the existence of strongly quantum advantageous, idler-free protocols for the discrimination of bosonic loss and environmental noise. This circumvents the necessity for idler assistance to achieve quantum advantage in some of the most relevant discrimination settings, significantly loosening practical requirements for prominent quantum-sensing applications.

Abstract We consider a quantum relay that is used by two parties to perform several continuous-variable protocols of quantum communication, from entanglement distribution (swapping and distillation) to quantum teleportation, and quantum key distribution. The theory of these protocols is suitably extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise in the bosonic environment. In the worst-case scenario where bipartite entanglement is completely lost at the relay, we show that the various protocols can be reactivated by the assistance of classical (separable) correlations in the environment. In fact, above a critical amount, these correlations are able to guarantee the distribution of a weaker form of entanglement (quadripartite), which can be localized by the relay into a stronger form (bipartite) that is exploitable by the parties. Our findings are confirmed by a proof-of-principle experiment where we show, for the first time, that memory effects in the environment can drastically enhance the performance of a quantum relay, well beyond the single-repeater bound for quantum and private communications.

Security analyses for trusted quantum random number generators usually consider only classical side-information. Here, the authors fill this gap by fully characterising the experimental apparatus of a homodyne-based QRNG, assuming that the vacuum fluctuations and noise are stationary and Gaussian.

The amount of information that a quantum channel can transmit is fundamentally bounded by the amount of noise in the channel. Here, the authors consider the realistic case with loss and thermal noise errors and prove that correlated multi-mode thermal states can achieve higher rates than single-mode ones.

It is not clear if the performance of a quantum lidar or radar, without an idler and only using Gaussian resources, could exceed the performance of a semiclassical setup based on coherent states and homodyne detection. Here we prove this is indeed the case by showing that an idler-free squeezed-based setup can beat this semiclassical benchmark. More generally, we show that probes whose displacement and squeezing are jointly optimized can strictly outperform coherent states with the same mean number of input photons for both the problems of quantum illumination and reading.

The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, we model the loss introduced at the repeater stations and then prove the corresponding limits. In the linear chain scenario we show that, by increasing the number of repeater stations, the maximum rate cannot overcome a quantity, which solely depends on the loss of a single station. We introduce a way of adapting the standard machinery for obtaining bounds to this realistic scenario. The difference is that whilst ultimate limits for any strategy can be derived given a fixed channel, when the repeaters introduce additional decoherence, then the effective overall channel is itself a function of the chosen repeater strategy (e.g., one-way versus two-way classical communication). Classes of repeater strategies can be analysed using additional modeling and the subsequent bounds can be interpreted as the optimal rate within that class.

The global interest in quantum networks stems from the security guaranteed by the laws of physics. The deployment of quantum networks means facing the challenges of scaling up the physical hardware and, more importantly, of scaling up all other network layers and optimally utilizing network resources. Here, we consider two related protocols and their experimental demonstrations on an eight-user quantum network test bed, and discuss their usefulness with the aid of example use cases. First, we consider an authentication-transfer protocol to manage a fundamental limitation of quantum communication—the need for a preshared key between every pair of users linked together on the quantum network. By temporarily trusting some intermediary nodes for a short period of time (

The development of a future global quantum communication network (or quantum Internet) will enable high-rate private communication and entanglement distribution over very long distances. However, the large-scale performance of ground-based quantum networks (which employ photons as information carriers through optical fibers) is fundamentally limited by fiber quality and link length, with the latter being a primary design factor for practical network architectures. While these fundamental limits are well established for arbitrary network topologies, the question of how to best design global architectures remains open. In this work, we introduce a large-scale quantum network model called weakly regular architectures. Such networks are capable of idealizing network connectivity, provide freedom to capture a broad class of spatial topologies, and remain analytically treatable. This allows us to investigate the effectiveness of large-scale networks with consistent connective properties and unveil critical conditions under which end-to-end rates remain optimal. Furthermore, through a strict performance comparison of ideal ground-based quantum networks with that of realistic satellite quantum communication protocols, we establish conditions for which satellites can be used to outperform fiber-based quantum infrastructure, rigorously proving the efficacy of satellite-based technologies for global quantum communications.

Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data are postprocessed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime, which requires the use of high-rate (nonbinary) low-density parity check codes. We implement all these steps in a python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.

We propose a multimode modulation scheme for continuous-variable (CV) quantum communications, which we call quantum pattern encoding. In this setting, classical information can be encoded into multimode patterns of discretely modulated coherent states, which form instances of a communicable image space. Communicators can devise arbitrarily complex encoding schemes that are degenerate and highly nonuniform, such that communication is likened to the task of pattern recognition. We explore initial communication schemes that exploit these techniques and that lead to an increased encoding complexity. We discuss the impact that this has on the role of a near-term quantum eavesdropper; formulating new realistic classes of attacks and secure communication rates.

Quantum classification and hypothesis testing (state and channel discrimination) are two tightly related subjects, the main difference being that the former is data driven: how to assign to quantum states ρ(x) the corresponding class c (or hypothesis) is learnt from examples during training, where x can be either tunable experimental parameters or classical data “embedded” into quantum states. Does the model generalize? This is the main question in any data-driven strategy, namely the ability to predict the correct class even of previously unseen states. Here we establish a link between quantum classification and quantum information theory, by showing that the accuracy and generalization capability of quantum classifiers depend on the (Rényi) mutual information I(C:Q) and I_{2}(X:Q) between the quantum state space Q and the classical parameter space X or class space C. Based on the above characterization, we then show how different properties of Q affect classification accuracy and generalization, such as the dimension of the Hilbert space, the amount of noise, and the amount of neglected information from X via, e.g., pooling layers. Moreover, we introduce a quantum version of the information bottleneck principle that allows us to explore the various trade-offs between accuracy and generalization. Finally, in order to check our theoretical predictions, we study the classification of the quantum phases of an Ising spin chain, and we propose the variational quantum information bottleneck method to optimize quantum embeddings of classical data to favor generalization.

Continuous variable (CV) quantum key distribution (QKD) provides a powerful setting for secure quantum communications, thanks to the use of room-temperature off-the-shelf optical devices and the potential to reach much higher rates than the standard discrete-variable counterpart. In this paper, we provide a general framework for studying the composable finite-size security of CV-QKD with Gaussian-modulated coherent-state protocols under various levels of trust for the loss and noise experienced by the parties. Our paper considers both wired (i.e., fiber-based) and wireless (i.e., free-space) quantum communications. In the latter case, we show that high key rates are achievable for short-range optical wireless (LiFi) in secure quantum networks with both fixed and mobile devices. Finally, we extend our investigation to microwave wireless (WiFi) discussing security and feasibility of CV-QKD for very short-range applications.

Quantum communications will be used to transmit entanglement and secure keys, but it is important to estimate their optimal transfer rates. Here the authors compute the fundamental limit of repeaterless quantum communications for the most relevant practical scenario.

Satellite quantum communications are emerging within the panorama of quantum technologies as a more effective strategy to distribute completely secure keys at very long distances, therefore playing an important role in the architecture of a large-scale quantum network. In this work, we apply and extend recent results in free-space quantum communications to determine the ultimate limits at which secret (and entanglement) bits can be distributed via satellites. Our study is comprehensive of the various practical scenarios, encompassing both downlink and uplink configurations, with satellites at different altitudes and zenith angles. It includes effects of diffraction, extinction, background noise, and fading, due to pointing errors and atmospheric turbulence (appropriately developed for slant distances). Besides identifying upper bounds, we also discuss lower bounds, i.e., achievable rates for key generation and entanglement distribution. In particular, we study the composable finite-size secret key rates that are achievable by protocols of continuous variable quantum key distribution, for both downlink and uplink, showing the feasibility of this approach for all configurations. Finally, we present a study with a sun-synchronous satellite, showing that its key distribution rate is able to outperform a ground chain of ideal quantum repeaters.

The study of free-space quantum communications requires tools from quantum information theory, optics, and turbulence theory. Here we combine these tools to bound the ultimate rates for key and entanglement distribution through a free-space link, where the propagation of quantum systems is generally affected by diffraction, atmospheric extinction, turbulence, pointing errors, and background noise. Besides establishing ultimate limits, we also show that the composable secret-key rate achievable by a suitable (pilot-guided and postselected) coherent-state protocol is sufficiently close to these limits, therefore showing the suitability of free-space channels for high-rate quantum key distribution. Our paper provides analytical tools for assessing the composable finite-size security of coherent-state protocols in general conditions from the standard assumption of a stable communication channel (as is typical in fiber-based connections) to the more challenging scenario of a fading channel (as is typical in free-space links).

We consider continuous-variable quantum key distribution with discrete-alphabet encodings. In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states. In this setting, we study the composable security in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks. Under this assumption, we can efficiently estimate the parameters of the channel via maximum likelihood estimators and bound the corresponding error in the final secret key rate.

Reliable methods for the classification and quantification of quantum entanglement are fundamental to understanding its exploitation in quantum technologies. One such method, known as separable neural network quantum states (SNNS), employs a neural network inspired parameterization of quantum states whose entanglement properties are explicitly programmable. Combined with generative machine learning methods, this ansatz allows for the study of very specific forms of entanglement which can be used to infer/measure entanglement properties of target quantum states. In this work, we extend the use of SNNS to mixed, multipartite states, providing a versatile and efficient tool for the investigation of intricately entangled quantum systems. We illustrate the effectiveness of our method through a number of examples, such as the computation of novel tripartite entanglement measures, and the approximation of ultimate upper bounds for qudit channel capacities.

Quantum hypothesis testing has shown the advantages that quantum resources can offer in the discrimination of competing hypothesis. Here, we apply this framework to optomechanical systems and fundamental physics questions. In particular, we focus on an optomechanical system composed of two cavities employed to perform quantum channel discrimination. We show that input squeezed optical noise, and feasible measurement schemes on the output cavity modes, allow to obtain an advantage with respect to any comparable classical schemes. We apply these results to the discrimination of models of spontaneous collapse of the wavefunction, highlighting the possibilities offered by this scheme for fundamental physics searches.

Quantum channels model many physical processes. For this reason, hypothesis testing between quantum channels is a fundamental task in quantum information theory. Here we consider the paradigmatic case of channel position finding, where the aim is to determine the position of a target quantum channel within a sequence of background channels. We explore this model in the setting of bosonic systems, considering Gaussian channels with the same transmissivity (or gain) but different levels of environmental noise. Thus, the goal of the problem becomes detecting the position of a target environment among a number of identical background environments, all acting on an input multimode system. We derive bounds for the ultimate error probability affecting this multiary discrimination problem and find an analytic condition for quantum advantage over protocols involving classical input states. We also design an explicit protocol that gives numerical bounds on the ultimate error probability and often achieves quantum advantage. Finally, we consider direct applications of the model for tasks of thermal imaging (finding a warmer pixel in a colder background) and quantum communication (for localizing a different level of noise in a sequence of lines or a frequency spectrum).

The field of quantum sensing aims at improving the detection and estimation of classical parameters that are encoded in physical systems by resorting to quantum sources of light and quantum detection strategies. The same approach can be used to improve the current classical measurements that are performed on biological systems. Here we consider the scenario of two bacteria (E. coli and Salmonella) growing in a Luria-Bertani broth and monitored by classical spectrophotometers. Their concentration can be related to the optical transmissivity via the Beer-Lambert-Bouguer's law and their growth curves can be described by means of Gompertz functions. Starting from experimental data points, we extrapolate the growth curves of the two bacteria and we study the theoretical performance that would be achieved with a quantum setup. In particular, we discuss how the bacterial growth can in principle be tracked by irradiating the samples with orders of magnitude fewer photons, identifying the clear superiority of quantum light in the early stages of growth. We then show the superiority and the limits of quantum resources in two basic tasks: (i) the early detection of bacterial growth and (ii) the early discrimination between two bacteria species.

We introduce a robust scheme for long-distance continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution in which we employ postselection between distant parties communicating through the medium of an untrusted relay. We perform a security analysis that allows for general transmissivity and thermal noise variance of each link, in which we assume that an eavesdropper performs a collective attack and controls the excess thermal noise in the channels. The introduction of postselection enables the parties to sustain a secret key rate over distances exceeding those of existing CV MDI protocols. In the worst-case scenario in which the relay is positioned equidistant between them, we find that the parties may communicate securely over a range of 14 km in standard optical fiber. Our protocol helps to overcome the rate-distance limitations of previously proposed CV MDI protocols while maintaining many of their advantages.

With the aim to loosen the entanglement requirements of quantum illumination, we study the performance of a family of Gaussian states at the transmitter, combined with an optimal and joint quantum measurement at the receiver. We find that maximal entanglement is not strictly necessary to achieve quantum advantage over the classical benchmark of a coherent-state transmitter, in both settings of symmetric and asymmetric hypothesis testing. While performing this quantum-classical comparison, we also investigate a suitable regime of parameters for potential short-range radar (or scanner) applications.

We consider the fundamental protocol of dense coding of classical information assuming that noise affects both the forward and backward communication lines between Alice and Bob. Assuming that this noise is described by the same quantum channel, we define its dense coding capacity by optimizing over all adaptive strategies that Alice can implement, while Bob encodes the information by means of Pauli operators. Exploiting techniques of channel simulation and protocol stretching, we are able to establish the dense coding capacity of Pauli channels in arbitrary finite dimension, with simple formulas for depolarizing and dephasing qubit channels.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

The task of classifying the entanglement properties of a multipartite quantum state poses a remarkable challenge due to the exponentially increasing number of ways in which quantum systems can share quantum correlations. Tackling such challenge requires a combination of sophisticated theoretical and computational techniques. In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine architecture, known as Neural Network Quantum States, whose entanglement properties can be deduced via a constrained, reinforcement learning procedure. In this way, Separable Neural Network States can be used to build entanglement witnesses for any target state.

We propose a method to improve the performance of two entanglement-based continuous-variable quantum key distribution protocols using noiseless linear amplifiers. The two entanglement-based schemes consist of an entanglement distribution protocol with an untrusted source and an entanglement swapping protocol with an untrusted relay. Simulation results show that the noiseless linear amplifiers can improve the performance of these two protocols, in terms of maximal transmission distances, when we consider small amounts of entanglement, as typical in realistic setups.

The benefits of entanglement can outlast entanglement itself. In quantum illumination, entanglement is employed to better detect reflecting objects in environments so noisy that all entanglement is destroyed. Here, we show that quantum discord—a more resilient form of quantum correlations—explains the resilience of quantum illumination. We introduce a quantitative relation between the performance gain in quantum illumination and the amount of discord used to encode information about the presence or absence of a reflecting object. This highlights discords role preserving the benefits of entanglement in entanglement breaking noise.

Combining two entanglement-breaking channels into a correlated-noise environment restores the distribution of entanglement. Surprisingly, this reactivation can be induced by the injection of separable correlations from the composite environment. In any dimension (finite or infinite), we can construct classically correlated ‘twirling’ environments which are entanglement-breaking in the transmission of single systems but entanglement-preserving when two systems are transmitted. Here entanglement is simply preserved by the existence of decoherence-free subspaces. Remarkably, even when such subspaces do not exist, a fraction of the input entanglement can still be distributed. This is found in separable Gaussian environments, where distillable entanglement is able to survive the two-mode transmission, despite being broken in any single-mode transmission by the strong thermal noise. In the Gaussian setting, entanglement restoration is a threshold process, occurring only after a critical amount of correlations has been injected. Such findings suggest new perspectives for distributing entanglement in realistic environments with extreme decoherence, identifying separable correlations and classical memory effects as physical resources for ‘breaking entanglement-breaking’.