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/r
adar where the input sources are semiclassical (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 Steins lemma. However, here we discuss that, for typical finite-size regimes, the second- and third-order expansions associated with this approach are not sufficient to prove quantum advantage.
Channel position finding is the task of determining the location of a single target channel amongst an ensemble of background channels. It has many potential applications, including quantum sensing, quantum reading and quantum spectroscopy. In partic
ular, it could allow for simple detection protocols to be extended to ones of measurement, for example, target ranging with quantum illumination. The use of quantum states and entanglement in such protocols have shown to yield quantum advantages over their optimal classical counterparts. Here we consider quantum channel position finding using sources specified by at most one single photon on average per mode, using the discrete variable formalism. By considering various quantum sources it is shown through the derivation of performance bounds that a quantum enhancement may be realised.
It is believed that the optimal performance of a quantum lidar or radar in the absence of an idler and only using Gaussian resources cannot exceed the performance of a semiclassical setup based on coherent states and homodyne detection. Here we dispr
ove this conjecture by showing that an idler-free squeezed-based setup can beat this 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.
An important theorem in Gaussian quantum information tells us that we can diagonalise the covariance matrix of any Gaussian state via a symplectic transformation. Whilst the diagonal form is easy to find, the process for finding the diagonalising sym
plectic can be more difficult, and a common, existing method requires taking matrix powers, which can be demanding analytically. Inspired by a recently presented technique for finding the eigenvectors of a Hermitian matrix from certain submatrix eigenvalues, we derive a similar method for finding the diagonalising symplectic from certain submatrix determinants, which could prove useful in Gaussian quantum information.
Since the invention of the laser in the 60s, one of the most fundamental communication channels has been the free-space optical channel. For this type of channel, a number of effects generally need to be considered, including diffraction, refraction,
atmospheric extinction, pointing errors and, most importantly, turbulence. Because of all these adverse features, the free-space channel is more difficult to study than a stable fiber-based link. For the same reasons, only recently it has been possible to establish the ultimate performances achievable in quantum communications via free-space channels, together with practical rates for continuous variable (CV) quantum key distribution (QKD). Differently from previous literature, mainly focused on the regime of weak turbulence, this work considers the free-space optical channel in the more challenging regime of moderate-to-strong turbulence, where effects of beam widening and breaking are more important than beam wandering. This regime may occur in long-distance free-space links on the ground, in uplink to high-altitude platform systems (HAPS) and, more interestingly, in downlink from near-horizon satellites. In such a regime we rigorously investigate ultimate limits for quantum communications and show that composable keys can be extracted using CV-QKD. In particular, we apply our results to downlink from satellites at large zenith angles, for which not only turbulence is strong but also refraction causes non-trivial effects in terms of trajectory elongation.
Quantum illumination (QI) theoretically promises up to a 6dB error-exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime which 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. In this work we outline what is the true classical benchmark for microwave QI using coherent states, providing new bounds on the error probability and closed formulae for the receiver operating characteristic (ROC), for both optimal (based on quantum relative entropy) and homodyne detection schemes. We also propose an alternative source generation procedure based on coherent states which demonstrates potential to reach classically optimal performances achievable in optical applications. We provide the same bounds and measures for the performance of such a source and discuss its potential utility in the future of room temperature quantum detection schemes in the microwave.
Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance for such pro
tocols. In this paper, we introduce a quantity that we call the relative fidelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose fidelity is greater than some minimum input fidelity and minimising this quantity over the valid pairs of states, we get the minimum relative fidelity for that input fidelity constraint. We are then able to lower bound the fidelity between the possible output states of any protocol acting on one of two possible channels in terms of the minimum relative fidelity. This allows us to bound the performance of the most general, adaptive discrimination and parameter estimation protocols. By finding a continuity bound for the relative fidelity, we also provide a simple confirmation that the quantum Fisher information (QFI) of the output of an $N$-use protocol is no more than $N^2$ times the one-shot QFI.
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 n
etworks (which employ photons as information carriers through optical-fibres) is fundamentally limited by the fibre quality and link length. While these fundamental limits are well established for arbitrary network architectures, the question of how to best design these global architectures remains open. In this work, we take a step forward in addressing this problem by modelling global quantum networks with weakly-regular architectures. Such networks are capable of idealising end-to-end performance whilst remaining sufficiently realistic. In this way, we may investigate the effectiveness of large-scale networks with consistent connective properties, and unveil the global conditions under which end-to-end rates remain analytically computable. Furthermore, by comparing the performance of ideal, ground-based quantum networks with satellite quantum communication protocols, we can establish conditions for which satellites can be used to outperform fibre-based quantum infrastructure.
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-sca
le 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.
While quantum illumination (QI) can offer a quantum-enhancement in target detection, its potential for performing target ranging remains unclear. With its capabilities hinging on a joint-measurement between a returning signal and its retained idler,
an unknown return time makes a QI-based protocol difficult to realise. This paper outlines a potential QI-based approach to quantum target ranging based on recent developments in multiple quantum hypothesis testing and quantum-enhanced channel position finding (CPF). Applying CPF to time bins, one finds an upper-bound on the error probability for quantum target ranging. However, using energetic considerations, we show that for such a scheme a quantum advantage may not physically be realised.
