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In this paper, we are concerned with the monotonic and symmetric properties of convex solutions to fully nonlinear elliptic systems. We mainly discuss Monge-Amp\`ere type systems for instance, considering \begin{equation*} \det(D^2u^i)=f^i(x,{\bf u},\nabla u^i), \ 1\leq i\leq m, \end{equation*} over bounded domains of various cases, including the bounded smooth simply connected domains and bounded tube shape domains in $\mathbb{R}^n$. We obtain monotonic and symmetric properties of the solutions to the problem with respect to the geometry of domains and the monotonic and symmetric properties of right-hand side terms. The proof is based on carefully using the moving plane method together with various maximum principles and Hopf's lemmas. The existence and uniqueness to an interesting example of such system is also discussed as an application of our results., Comment: comments are welcome! arXiv admin note: substantial text overlap with arXiv:2404.01185

In this paper, we study the following fully nonlinear elliptic equations \begin{equation*} \left\{\begin{array}{rl} \left(S_{k}(D^{2}u)\right)^{\frac1k}=\lambda f(-u) & in\quad\Omega \\ u=0 & on\quad \partial\Omega\\ \end{array} \right. \end{equation*} and coupled systems \begin{equation*} \left\{\begin{array}{rl} (S_{k}(D^{2}u))^\frac1k=\lambda g(-u,-v) & in\quad\Omega \\ (S_{k}(D^{2}v))^\frac1k=\lambda h(-u,-v) & in\quad\Omega \\ u=v=0 & on\quad \partial\Omega\\ \end{array} \right. \end{equation*} dominated by $k$-Hessian operators, where $\Omega$ is a $(k$-$1)$-convex bounded domain in $\mathbb{R}^{N}$, $\lambda$ is a non-negative parameter, $f:\left[0,+\infty\right)\rightarrow\left[0,+\infty\right)$ is a continuous function with zeros only at $0$ and $g,h:\left[0,+\infty\right)\times \left[0,+\infty\right)\rightarrow \left[0,+\infty\right)$ are continuous functions with zeros only at $(\cdot,0)$ and $(0,\cdot)$. We determine the interval of $\lambda$ about the existence, non-existence, uniqueness and multiplicity of $k$-convex solutions to the above problems according to various cases of $f,g,h$, which is a complete supplement to the known results in previous literature. In particular, the above results are also new for Laplacian and Monge-Amp\`ere operators. We mainly use bifurcation theory, a-priori estimates, various maximum principles and technical strategies in the proof., Comment: comments are welcome!

In this paper, we are concerned with the monotonic and symmetric properties of convex solutions Monge-Amp\`ere systems for instance, considering \begin{equation*} \det(D^2u^i)=f^i(x,{\bf u},\nabla u^i), \ 1\leq i\leq m, \end{equation*} over unbounded domains of various cases, including the whole spaces $\mathbb{R}^n$, the half spaces $\mathbb{R}^n_+$ and the unbounded tube shape domains in $\mathbb{R}^n$. We obtain monotonic and symmetric properties of the solutions to the problem with respect to the geometry of domains and the monotonic and symmetric properties of right-hand side terms. The proof is based on carefully using the moving plane method together with various maximum principles and Hopf's lemmas., Comment: comments are welcome!

Photon number resolving (PNR) capability is very important in many optical applications, including quantum information processing, fluorescence detection, and few-photon-level ranging and imaging. Superconducting nanowire single-photon detectors (SNSPDs) with a multipixel interleaved architecture give the array an excellent spatial PNR capability. However, the signal-to-noise ratio (SNR) of the photon number resolution (SNRPNR) of the array will be degraded with increasing the element number due to the electronic noise in the readout circuit, which limits the PNR resolution as well as the maximum PNR number. In this study, a 16-element interleaved SNSPD array was fabricated, and the PNR capability of the array was investigated and analyzed. By introducing a level comparator circuit (LCC), the SNRPNR of the detector array was improved over a factor of four. In addition, we performed a statistical analysis of the photon number on this SNSPD array with LCC, showing that the LCC method effectively enhances the PNR resolution. Besides, the system timing jitter of the detector was reduced from 90 ps to 72 ps due to the improved electrical SNR., Comment: 8 pages, 7 figures

Existing vehicle re-identification methods mainly rely on the single query, which has limited information for vehicle representation and thus significantly hinders the performance of vehicle Re-ID in complicated surveillance networks. In this paper, we propose a more realistic and easily accessible task, called multi-query vehicle Re-ID, which leverages multiple queries to overcome viewpoint limitation of single one. Based on this task, we make three major contributions. First, we design a novel viewpoint-conditioned network (VCNet), which adaptively combines the complementary information from different vehicle viewpoints, for multi-query vehicle Re-ID. Moreover, to deal with the problem of missing vehicle viewpoints, we propose a cross-view feature recovery module which recovers the features of the missing viewpoints by learnt the correlation between the features of available and missing viewpoints. Second, we create a unified benchmark dataset, taken by 6142 cameras from a real-life transportation surveillance system, with comprehensive viewpoints and large number of crossed scenes of each vehicle for multi-query vehicle Re-ID evaluation. Finally, we design a new evaluation metric, called mean cross-scene precision (mCSP), which measures the ability of cross-scene recognition by suppressing the positive samples with similar viewpoints from same camera. Comprehensive experiments validate the superiority of the proposed method against other methods, as well as the effectiveness of the designed metric in the evaluation of multi-query vehicle Re-ID.

Quantum key distribution can provide unconditionally secure key exchange for remote users in theory. In practice, however, in most quantum key distribution systems, quantum hackers might steal the secure keys by listening to the side channels in the source, such as the photon frequency spectrum, emission time, propagation direction, spatial angular momentum, and so on. It is hard to prevent such kinds of attacks because side channels may exist in any of the encoding space whether the designers take care of or not. Here we report an experimental realization of a side-channel-free quantum key distribution protocol which is not only measurement-device-independent, but also immune to all side-channel attacks in the source. We achieve a secure key rate of 4.80e-7 per pulse through 50 km fiber spools., Comment: 23 pages, 5 figures

Quantum key distribution endows people with information-theoretical security in communications. Twin-field quantum key distribution (TF-QKD) has attracted considerable attention because of its outstanding key rates over long distances. Recently, several demonstrations of TF-QKD have been realized. Nevertheless, those experiments are implemented in the laboratory, remaining a critical question about whether the TF-QKD is feasible in real-world circumstances. Here, by adopting the sending-or-not-sending twin-field QKD (SNS-TF-QKD) with the method of actively odd parity pairing (AOPP), we demonstrate a field-test QKD over 428~km deployed commercial fiber and two users are physically separated by about 300~km in a straight line. To this end, we explicitly measure the relevant properties of the deployed fiber and develop a carefully designed system with high stability. The secure key rate we achieved breaks the absolute key rate limit of repeater-less QKD. The result provides a new distance record for the field test of both TF-QKD and all types of fiber-based QKD systems. Our work bridges the gap of QKD between laboratory demonstrations and practical applications, and paves the way for intercity QKD network with high-speed and measurement-device-independent security.

Distributed quantum sensing can provide quantum-enhanced sensitivity beyond the shot-noise limit (SNL) for sensing spatially distributed parameters. To date, distributed quantum sensing experiments have been mostly accomplished in laboratory environments without a real space separation for the sensors. In addition, the post-selection is normally assumed to demonstrate the sensitivity advantage over the SNL. Here, we demonstrate distributed quantum sensing in field and show the unconditional violation (without post-selection) of SNL up to 0.916 dB for the field distance of 240 m. The achievement is based on a loophole free Bell test setup with entangled photon pairs at the averaged heralding efficiency of 73.88%. Moreover, to test quantum sensing in real life, we demonstrate the experiment for long distances (with 10-km fiber) together with the sensing of a completely random and unknown parameter. The results represent an important step towards a practical quantum sensing network for widespread applications., Comment: 8 pages, 5 figures

Superconducting nanowire single-photon detector (SNSPD) with near-unity system efficiency is a key enabling, but still elusive technology for numerous quantum fundamental theory verifications and quantum information applications. The key challenge is to have both a near-unity photon-response probability and absorption efficiency simultaneously for the meandered nanowire with a finite filling ratio, which is more crucial for NbN than other superconducting materials (e.g., WSi) with lower transition temperatures. Here, we overcome the above challenge and produce NbN SNSPDs with a record system efficiency by replacing a single-layer nanowire with twin-layer nanowires on a dielectric mirror. The detector at 0.8 K shows a maximal system detection efficiency (SDE) of 98% at 1590 nm and a system efficiency of over 95% in the wavelength range of 1530-1630 nm. Moreover, the detector at 2.1K demonstrates a maximal SDE of 95% at 1550 nm using a compacted two-stage cryocooler. This type of detector also shows the robustness against various parameters, such as the geometrical size of the nanowire, and the spectral bandwidth, enabling a high yield of 73% (36%) with an SDE of >80% (90%) at 2.1K for 45 detectors fabricated in the same run. These SNSPDs made of twin-layer nanowires are of important practical significance for batch production., Comment: 17 pages, 13 figures

Measurement-device-independent quantum key distribution (MDI-QKD), based on two-photon interference, is immune to all attacks against the detection system and allows a QKD network with untrusted relays. Since the MDI-QKD protocol was proposed, fibre-based implementations have been rapidly developed towards longer distance, higher key rates, and network verification. However, owing to the effect of atmospheric turbulence, MDI-QKD over free-space channel remains experimentally challenging. Here, by developing the robust adaptive optics system, high precision time synchronization and frequency locking between independent photon sources located far apart, we realised the first free-space MDI-QKD over a 19.2-km urban atmospheric channel, which well exceeds the effective atmospheric thickness. Our experiment takes the first step towards satellite-based MDI-QKD. Moreover, the technology developed here opens the way to quantum experiments in free space involving long-distance interference of independent single photons., Comment: 14 pages, 3 figures

Twin field quantum key distribution promises high key rates at long distance to beat the rate distance limit. Here, applying the sending or not sending TF QKD protocol, we experimentally demonstrate a secure key distribution breaking the absolute key rate limit of repeaterless QKD over 509 km, 408 km ultra-low loss optical fibre and 350 km standard optical fibre. Two independent lasers are used as the source with remote frequency locking technique over 500 km fiber distance; Practical optical fibers are used as the optical path with appropriate noise filtering; And finite key effects are considered in the key rate analysis. The secure key rates obtained at different distances are more than 5 times higher than the conditional limit of repeaterless QKD, a bound value assuming the same detection loss in the comparison. The achieved secure key rate is also higher than that a traditional QKD protocol running with a perfect repeaterless QKD device and even if an infinite number of sent pulses. Our result shows that the protocol and technologies applied in this experiment enable TF QKD to achieve high secure key rate at long distribution distance, and hence practically useful for field implementation of intercity QKD., Comment: 17 pages, 10 figures and 8 tables

Quantum key distribution (QKD offers a long-term solution to establish information-theoretically secure keys between two distant users. In practice, with a careful characterization of quantum sources and the decoy-state method, measure-device-independent quantum key distribution (MDI-QKD) provides secure key distribution. While short-distance fibre-based QKD has already been available for real-life implementation, the bottleneck of practical QKD lies on the limited transmission distance. Due to photon losses in transmission, it was believed that the key generation rate is bounded by a linear function of the channel transmittance, $O(\eta)$, without a quantum repeater, which puts an upper bound on the maximal secure transmission distance. Interestingly, a new phase-encoding MDI-QKD scheme, named twin-field QKD, has been suggested to beat the linear bound, while another variant, named phase-matching quantum key distribution (PM-QKD), has been proven to have a quadratic key-rate improvement, $O(\sqrt{\eta})$. In reality, however, the intrinsic optical mode mismatch of independent lasers, accompanied by phase fluctuation and drift, impedes the successful experimental implementation of the new schemes. Here, we solve this problem with the assistance of the laser injection technique and the phase post-compensation method. In the experiment, the key rate surpasses the linear key-rate bound via 302 km and 402 km commercial-fibre channels, achieving a key rate over 4 orders of magnitude higher than the existing results in literature. Furthermore, with a 502 km ultralow-loss fibre, our system yields a secret key rate of 0.118 bps. We expect this new type of QKD schemes to become a new standard for future QKD., Comment: 16 pages, 7 figures

Ensuring the non-entanglement-breaking (non-EB) property of quantum channels is crucial for the effective distribution and storage of quantum states. However, a practical method for direct and accurate certification of the non-EB feature is highly desirable. Here, we propose and verify a realistic source based measurement device independent certification of non-EB channels. Our method is resilient to repercussions on the certification from experimental conditions, such as multiphotons and imperfect state preparation, and can be implemented with information incomplete set. We achieve good agreement between experimental outcomes and theoretical predictions, which is validated by the expected results of the ideal semi-quantum signaling game, and accurately certify the non-EB channels. Furthermore, our approach is highly robust to effects from noise. Therefore, the proposed approach can be expected to play a significant role in the design and evaluation of realistic quantum channels., Comment: 13 pages, 5 figures. Manuscript rewritten, accepted by PRL. Comments are welcome

Gaussian Boson sampling (GBS) provides a highly efficient approach to make use of squeezed states from parametric down-conversion to solve a classically hard-to-solve sampling problem. The GBS protocol not only significantly enhances the photon generation probability, compared to standard boson sampling with single photon Fock states, but also links to potential applications such as dense subgraph problems and molecular vibronic spectra. Here, we report the first experimental demonstration of GBS using squeezed-state sources with simultaneously high photon indistinguishability and collection efficiency. We implement and validate 3-, 4- and 5-photon GBS with high sampling rates of 832 kHz, 163 kHz and 23 kHz, respectively, which is more than 4.4, 12.0, and 29.5 times faster than the previous experiments. Further, we observe a quantum speed-up on a NP-hard optimization problem when comparing with simulated thermal sampler and uniform sampler., Comment: 12 pages, 4 figures, published online on 2nd April 2019