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One-way functions are fundamental to classical cryptography and their existence remains a longstanding problem in computational complexity theory. Recently, a provable quantum one-way function has been identified, which maintains its one-wayness even with unlimited computational resources. Here, we extend the mathematical definition of functions to construct a generalized one-way function by virtually measuring the qubit of provable quantum one-way function and randomly assigning the corresponding measurement outcomes with identical probability. Remarkably, using this generalized one-way function, we have developed an unconditionally secure key distribution protocol based solely on classical data processing, which can then utilized for secure encryption and signature. Our work highlights the importance of information in characterizing quantum systems and the physical significance of the density matrix. We demonstrate that probability theory and randomness are effective tools for countering adversaries with unlimited computational capabilities., Comment: 16 pages, 3 figures, 1 table

Key distribution plays a fundamental role in cryptography. Currently, the quantum scheme stands as the only known method for achieving unconditionally secure key distribution. This method has been demonstrated over distances of 508 and 1002 kilometers in the measurement-device-independent and twin-field configurations, respectively. However, quantum key distribution faces transmission distance issues and numerous side channel attacks since the basic physical picture requires the use of quantum channels between users. Even when quantum repeater and quantum constellation are used, commercializing quantum cryptography on a large scale remains unattainable due to the considerable expense and significant technical hurdles associated with establishing a global quantum network and facilitating mobile quantum communication. Here, by discovering the provable quantum one-way function, we propose another key distribution scheme with unconditional security, named probability key distribution, that promises users between any two distances to generate a fixed and high secret key rate. There are no quantum channels for exchanging quantum signals between two legitimate users. Non-local entangled states can be generated, identified and measured in the equivalent virtual protocol and can be used to extract secret keys. We anticipate that this discovery presents a paradigm shift in achieving unconditionally secure cryptography, thereby facilitating its widespread application on a global scale., Comment: 23 pages, 3 figures, 1 table

The large-scale deployment of quantum secret sharing (QSS) in quantum networks is currently challenging due to the requirements for the generation and distribution of multipartite entanglement states. Here we present an efficient source-independent QSS protocol utilizing entangled photon pairs in quantum networks. Through the post-matching method, which means the measurement events in the same basis are matched, the key rate is almost independent of the number of participants. In addition, the unconditional security of our QSS against internal and external eavesdroppers can be proved by introducing an equivalent virtual protocol. Our protocol has great performance and technical advantages in future quantum networks., Comment: 13 pages, 9 figures

The idea of post-measurement coincidence pairing simplifies substantially long-distance, repeater-like quantum key distribution (QKD) by eliminating the need for tracking the differential phase of the users' lasers. However, optical frequency tracking remains necessary and can become a severe burden in future deployment of multi-node quantum networks. Here, we resolve this problem by referencing each user's laser to an absolute frequency standard and demonstrate a practical post-measurement pairing QKD with excellent long-term stability. We confirm the setup's repeater-like behavior and achieve a finite-size secure key rate (SKR) of 15.94 bit/s over 504 km fiber, which overcomes the absolute repeaterless bound by 1.28 times. Over a fiber length 100 km, the setup delivers an impressive SKR of 285.68 kbit/s. Our work paves the way towards an efficient muti-user quantum network with the local frequency standard.

The development of quantum networks is paramount towards practical and secure communications. Quantum digital signatures (QDS) offer an information-theoretically secure solution for ensuring data integrity, authenticity, and non-repudiation, rapidly growing from proof-of-concept to robust demonstrations. However, previous QDS systems relied on expensive and bulky optical equipment, limiting large-scale deployment and reconfigurable networking construction. Here, we introduce and verify a chip-based QDS network, placing the complicated and expensive measurement devices in the central relay while each user needs only a low-cost transmitter. We demonstrate the network with a three-node setup using an integrated encoder chip and decoder chip. By developing a 1-decoy-state one-time universal hash-QDS protocol, we achieve a maximum signature rate of 0.0414 times per second for a 1 Mbit file over fiber distances up to 200 km, surpassing all current state-of-the-art QDS experiments. This study validates the feasibility of chip-based QDS, paving the way for large-scale deployment and integration with existing fiber infrastructure., Comment: 11 pages, 6 figures

Quantum digital signatures (QDSs), which distribute and measure quantum states by key generation protocols and then sign messages via classical data processing, are a key area of interest in quantum cryptography. However, the practical implementation of a QDS network has many challenges, including complex interference technical requirements, linear channel loss of quantum state transmission, and potential side-channel attacks on detectors. Here, we propose an asynchronous measurement-device-independent (MDI) QDS protocol with asynchronous two-photon interference strategy and one-time universal hashing method. The two-photon interference approach protects our protocol against all detector side-channel attacks and relaxes the difficulty of experiment implementation, while the asynchronous strategy effectively reduces the equivalent channel loss to its square root. Compared to previous MDI-QDS schemes, our protocol shows several orders of magnitude performance improvements and doubling of transmission distance when processing multi-bit messages. Our findings present an efficient and practical MDI-QDS scheme, paving the way for large-scale data processing with non-repudiation in quantum networks., Comment: 17 pages, 5 figures, accepted by Physical Review A

Quantum digital signatures (QDS), which utilize correlated bit strings among sender and recipients, guarantee the authenticity, integrity and non-repudiation of classical messages based on quantum laws. Continuous-variable (CV) quantum protocol with heterodyne and homodyne measurement has obvious advantages of low-cost implementation and easy wavelength division multiplexing. However, security analyses in previous researches are limited to the proof against collective attacks in finite-size scenarios. Moreover, existing multi-bit CV QDS schemes have primarily focused on adapting single-bit protocols for simplicity of security proof, often sacrificing signature efficiency. Here, we introduce a CV QDS protocol designed to withstand general coherent attacks through the use of a cutting-edge fidelity test function, while achieving high signature efficiency by employing a refined one-time universal hashing signing technique. Our protocol is proved to be robust against finite-size effects and excess noise in quantum channels. In simulation, results demonstrate a significant reduction of over 6 orders of magnitude in signature length for a megabit message signing task compared to existing CV QDS protocols and this advantage expands as the message size grows. Our work offers a solution with enhanced security and efficiency, paving the way for large-scale deployment of CV QDS in future quantum networks., Comment: 18 pages, 8 figures

Quantum conferencing enables multiple nodes within a quantum network to share a secure group key for private message broadcasting. The key rate, however, is limited by the repeaterless capacity to distribute multiparticle entangled states across the network. Currently, in the finite-size regime, no feasible schemes utilizing existing experimental techniques can overcome the fundamental rate-distance limit of quantum conferencing in quantum networks without repeaters. Here, we propose a practical, multi-field scheme that breaks this limit, involving virtually establishing Greenberger-Horne-Zeilinger states through post-measurement coincidence matching. This proposal features a measurement-device-independent characteristic and can directly scale to support any number of users. Simulations show that the fundamental limitation on the group key rate can be overcome in a reasonable running time of sending $10^{14}$ pulses. We predict that it offers an efficient design for long-distance broadcast communication in future quantum networks., Comment: 20 pages, 6 figures

Quantum conference key agreement (QCKA) enables the unconditional secure distribution of conference keys among multiple participants. Due to challenges in high-fidelity preparation and long-distance distribution of multi-photon entanglement, entanglement-based QCKA is facing severe limitations in both key rate and scalability. Here, we propose a source-independent QCKA scheme utilizing the post-matching method, feasible within the entangled photon pair distribution network. We introduce an equivalent distributing virtual multi-photon entanglement protocol for providing the unconditional security proof even in the case of coherent attacks. For the symmetry star-network, comparing with previous $n$-photon entanglement protocol, the conference key rate is improved from $O(\eta^{n})$ to $O(\eta^{2})$, where $\eta$ is the transmittance from the entanglement source to one participant. Simulation results show that the performance of our protocol has multiple orders of magnitude advantages in the intercity distance. We anticipate that our approach will demonstrate its potential in the implementation of quantum networks., Comment: 10 pages, 6 figures

Quantum conference key agreement facilitates secure communication among multiple parties through multipartite entanglement and is anticipated to be an important cryptographic primitive for future quantum networks. However, the experimental complexity and low efficiency associated with the synchronous detection of multipartite entangled states have significantly hindered their practical application. In this work, we propose a measurement-device-independent conference key agreement protocol that utilizes asynchronous Greenberger-Horne-Zeilinger state measurement.This approach achieves a linear scaling of the conference key rate among multiple parties, exhibiting performance similar to that of the single-repeater scheme in quantum networks. The asynchronous measurement strategy bypasses the need for complex global phase locking technologies, concurrently extending the intercity transmission distance with composable security in the finite key regime. Additionally, our work also showcases the advantages of the asynchronous pairing concept in multiparty quantum entanglement., Comment: 21 pages, 7 figures

Satellite-to-ground quantum communication constitutes the cornerstone of the global quantum network, heralding the advent of the future of quantum information. Continuous-variable quantum key distribution is a strong candidate for space-ground quantum communication due to its simplicity, stability, and ease of implementation, especially for the robustness of space background light noise. Recently, the discrete-modulated continuous-variable protocol has garnered increased attention, owing to its lower implementation requirements, acceptable security key rate, and pronounced compatibility with extant infrastructures. Here, we derive key rates for discrete-modulated continuous-variable quantum key distribution protocols in free-space channel environments across various conditions through numerical simulation, revealing the viability of its application in satellite-to-ground communication., Comment: 12 pages, 6 figures

Quantum communication networks are crucial for both secure communication and cryptographic networked tasks. Building quantum communication networks in a scalable and cost-effective way is essential for their widespread adoption, among which a stable and miniaturized high-quality quantum light source is a key component. Here, we establish a complete polarization entanglement-based fully connected network, which features an ultrabright integrated Bragg reflection waveguide quantum source, managed by an untrusted service provider, and a streamlined polarization analysis module, which requires only one single-photon detector for each end user. We perform a continuously working quantum entanglement distribution and create correlated bit strings between users. Within the framework of one-time universal hashing, we provide the first experimental implementation of source-independent quantum digital signatures using imperfect keys circumventing the necessity for private amplification. More importantly, we further beat the 1/3 fault-tolerance bound in Byzantine agreement, achieving unconditional security without relying on sophisticated techniques. Our results offer an affordable and practical route for addressing consensus challenges within the emerging quantum network landscape.

With the contemporary digital technology approaching, deep neural networks are emerging as the foundational algorithm of the artificial intelligence boom. Whereas, the evolving social demands have been emphasizing the necessity of novel methodologies to substitute traditional neural networks. Concurrently, the advent of the post-Moore era has spurred the development of quantum-inspired neural networks with outstanding potentials at certain circumstances. Nonetheless, a definitive evaluating system with detailed metrics is tremendously vital and indispensable owing to the vague indicators in comparison between the novel and traditional deep learning models at present. Hence, to improve and evaluate the performances of the novel neural networks more comprehensively in complex and unpredictable environments, we propose two hybrid quantum-inspired neural networks which are rooted in residual and dense connections respectively for pattern recognitions with completeness representation theory for model assessment. Comparative analyses against pure classical models with detailed frameworks reveal that our hybrid models with lower parameter complexity not only match the generalization power of pure classical models, but also outperform them notably in resistance to parameter attacks with various asymmetric noises. Moreover, our hybrid models indicate unique superiority to prevent gradient explosion problems through theoretical argumentation. Eventually, We elaborate on the application scenarios where our hybrid models are applicable and efficient, which paves the way for their industrialization and commercialization., Comment: 12 pages for main paper with 13-page supplementary materials with a hyperlink in the last page of the main paper

Resonance fluorescence (RF) of a two-level emitter displays persistently anti-bunching irrespective of the excitation intensity, but inherits the driving laser's linewidth under weak excitation. These properties are commonly explained disjoinedly as the emitter's single photon saturation or passively scattering light, until a recent theory attributes anti-bunching to the laser-like spectrum's interference with the incoherently scattered light. However, the theory implies higher-order scattering processes, and led to an experiment purporting to validate an atom's simultaneous scattering of two photons. If true, it could complicate RF's prospects in quantum information applications. Here, we propose a unified model that treats all RF photons as spontaneous emission, one at a time, and can explain simultaneously both the RF's spectral and correlation properties. We theoretically derive the excitation power dependencies, with the strongest effects measurable at the single-photon incidence level, of the first-order coherence of the whole RF and super-bunching of the spectrally filtered, followed by experimental confirmation on a semiconductor quantum dot micro-pillar device. Furthermore, our model explains peculiar coincidence bunching observed in phase-dependent two-photon interference experiments. Our work provides novel understandings of coherent light-matter interaction and may stimulate new applications., Comment: Equation 4 is updated to cover all two-level emitters, with or without a cavity

The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In this paper we investigate R\'{e}nyi entropic uncertainty relations (EURs) in the scenario where measurements on individual copies of a quantum system are selected with nonuniform probabilities. In contrast with EURs that characterize an observer's overall lack of information about outcomes with respect to a collection of measurements, we establish state-dependent lower bounds on the weighted sum of entropies over multiple measurements. Conventional EURs thus correspond to the special cases when all weights are equal, and in such cases, we show our results are generally stronger than previous ones. Moreover, taking the entropic steering criterion as an example, we numerically verify that our EURs could be advantageous in practical quantum tasks by optimizing the weights assigned to different measurements. Importantly, this optimization does not require quantum resources and is efficiently computable on classical computers., Comment: 12 pages (including 7 pages in the main text),5 figures

Coherent-one-way (COW) quantum key distribution (QKD) is a significant communication protocol that has been implemented experimentally and deployed in practical products due to its simple equipment requirements. However, existing security analyses of COW-QKD either provide a short transmission distance or lack immunity against coherent attacks in the finite-key regime. In this paper, we present a tight finite-key security analysis within the universally composable framework for a variant of COW-QKD, which has been proven to extend the secure transmission distance in the asymptotic case. We combine the quantum leftover hash lemma and entropic uncertainty relation to derive the key rate formula. When estimating statistical parameters, we use the recently proposed Kato's inequality to ensure security against coherent attacks and achieve a higher key rate. Our paper confirms the security and feasibility of COW-QKD for practical application and lays the foundation for further theoretical study and experimental implementation., Comment: 15 pages, 7 figures

E-commerce, a type of trading that occurs at a high frequency on the Internet, requires guaranteeing the integrity, authentication and non-repudiation of messages through long distance. As current e-commerce schemes are vulnerable to computational attacks, quantum cryptography, ensuring information-theoretic security against adversary's repudiation and forgery, provides a solution to this problem. However, quantum solutions generally have much lower performance compared to classical ones. Besides, when considering imperfect devices, the performance of quantum schemes exhibits a significant decline. Here, for the first time, we demonstrate the whole e-commerce process of involving the signing of a contract and payment among three parties by proposing a quantum e-commerce scheme, which shows resistance of attacks from imperfect devices. Results show that with a maximum attenuation of 25 dB among participants, our scheme can achieve a signature rate of 0.82 times per second for an agreement size of approximately 0.428 megabit. This proposed scheme presents a promising solution for providing information-theoretic security for e-commerce., Comment: 19 pages, 5 figures, 5 tables

Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model for quantum neural computing using (classically-controlled) single-qubit operations and measurements on real-world quantum systems with naturally occurring environment-induced decoherence, which greatly reduces the difficulties of physical implementations. Our model circumvents the problem that the state-space size grows exponentially with the number of neurons, thereby greatly reducing memory requirements and allowing for fast optimization with traditional optimization algorithms. We benchmark our model for handwritten digit recognition and other nonlinear classification tasks. The results show that our model has an amazing nonlinear classification ability and robustness to noise. Furthermore, our model allows quantum computing to be applied in a wider context and inspires the earlier development of a quantum neural computer than standard quantum computers., Comment: 10 pages, 6 figures

The linear constraint of secret key rate capacity is overcome by the tiwn-field quantum key distribution (QKD). However, the complex phase-locking and phase-tracking technique requirements throttle the real-life applications of twin-field protocol. The asynchronous measurement-device-independent (AMDI) QKD or called mode-pairing QKD protocol can relax the technical requirements and keep the similar performance of twin-field protocol. Here, we propose an AMDI-QKD protocol with a nonclassical light source by changing the phase-randomized weak coherent state to a phase-randomized coherent-state superposition in the signal state time window. Simulation results show that our proposed hybrid source protocol significantly enhances the key rate of the AMDI-QKD protocol, while exhibiting robustness to imperfect modulation of nonclassical light sources., Comment: 9 pages, 4 figures

Quantum secret sharing (QSS) is one of the basic communication primitives in future quantum networks which addresses part of the basic cryptographic tasks of multiparty communication and computation. Nevertheless, it is a challenge to provide a practical QSS protocol with security against general attacks. A QSS protocol that balances security and practicality is still lacking. Here, we propose a QSS protocol with simple phase encoding of coherent states among three parties. Removing the requirement of impractical entangled resources and the need for phase randomization, our protocol can be implemented with accessible technology. We provide the finite-key analysis against coherent attacks and implement a proof-of-principle experiment to demonstrate our scheme's feasibility. Our scheme achieves a key rate of 85.3 bps under a 35 dB channel loss. Combined with security against general attacks and accessible technology, our protocol is a promising candidate for practical multiparty quantum communication networks., Comment: 10 pages, 5 figures, 3 tables, accepted by Sci. China-Phys. Mech. Astron

Quantum key distribution provides a promising solution for sharing secure keys between two distant parties with unconditional security. Nevertheless, quantum key distribution is still severely threatened by the imperfections of devices. In particular, the classical pulse correlation threatens security when sending decoy states. To address this problem and simplify experimental requirements, we propose a phase-matching quantum key distribution protocol without intensity modulation. Instead of using decoy states, we propose a novel method to estimate the theoretical upper bound on the phase error rate contributed by even-photon-number components. Simulation results show that the transmission distance of our protocol could reach 305 km in telecommunication fiber. Furthermore, we perform a proof-of-principle experiment to demonstrate the feasibility of our protocol, and the key rate reaches 22.5 bps under a 45 dB channel loss. Addressing the security loophole of pulse intensity correlation and replacing continuous random phase with 6 or 8 slices random phase, our protocol provides a promising solution for constructing quantum networks., Comment: Comments are welcome! 12 pages, 6 figures

The new variant of measurement-device-independent quantum key distribution (MDI-QKD), called asynchronous MDI-QKD or mode-pairing MDI-QKD, offers similar repeater-like rate-loss scaling but has the advantage of simple technology implementation by exploiting an innovative post-measurement pairing technique. We herein present an evaluation of the practical aspects of decoy-state asynchronous MDI-QKD. To determine its effectiveness, we analyze the optimal method of decoy-state calculation and examine the impact of asymmetrical channels and multi-user networks. Our simulations show that, under realistic conditions, aynchronous MDI-QKD can furnish the highest key rate with MDI security as compared to other QKD protocols over distances ranging from 50 km to 480 km. At fiber distances of 50 km and 100 km, the key rates attain 6.02 Mbps and 2.29 Mbps respectively, which are sufficient to facilitate real-time one-time-pad video encryption. Our findings indicate that experimental implementation of asynchronous MDI-QKD in intercity networks can be both practical and efficient., Comment: 15 pages, 4 figures

Quantum digital signatures (QDS), generating correlated bit strings among three remote parties for signatures through quantum law, can guarantee non-repudiation, authenticity, and integrity of messages. Recently, one-time universal hashing QDS framework, exploiting the quantum asymmetric encryption and universal hash functions, has been proposed to significantly improve the signature rate and ensure unconditional security by directly signing the hash value of long messages. However, similar to quantum key distribution, this framework utilizes keys with perfect secrecy by performing privacy amplification that introduces cumbersome matrix operations, thereby consuming large computational resources, causing delays and increasing failure probability. Here, we prove that, different from private communication, imperfect quantum keys with limited information leakage can be used for digital signatures and authentication without compromising the security while having eight orders of magnitude improvement on signature rate for signing a megabit message compared with conventional single-bit schemes. This study significantly reduces the delay for data postprocessing and is compatible with any quantum key generation protocols. In our simulation, taking two-photon twin-field key generation protocol as an example, QDS can be practically implemented over a fiber distance of 650 km between the signer and receiver. For the first time, this study offers a cryptographic application of quantum keys with imperfect secrecy and paves a way for the practical and agile implementation of digital signatures in a future quantum network., Comment: 20 pages, 7 figures

Secure key rate (SKR) of point-point quantum key distribution (QKD) is fundamentally bounded by the rate-loss limit. Recent breakthrough of twin-field (TF) QKD can overcome this limit and enables long distance quantum communication, but its implementation necessitates complex global phase tracking and requires strong phase references which not only add to noise but also reduce the duty cycle for quantum transmission. Here, we resolve these shortcomings, and importantly achieve even higher SKRs than TF-QKD, via implementing an innovative but simpler measurement-device-independent QKD which realizes repeater-like communication through asynchronous coincidence pairing. Over 413 and 508 km optical fibers, we achieve finite-size SKRs of 590.61 and 42.64 bit/s, which are respectively 1.80 and 4.08 times of their corresponding absolute rate limits. Significantly, the SKR at 306 km exceeds 5 kbit/s and meets the bitrate requirement for live one-time-pad encryption of voice communication. Our work will bring forward economical and efficient intercity quantum-secure networks., Comment: 29 pages, 10 figures, 3 tables

Quantum network applications like distributed quantum computing and quantum secret sharing present a promising future network equipped with quantum resources. Entanglement generation and distribution over long distances is critical and unavoidable to utilize quantum technology in a fully-connected network. The distribution of bipartite entanglement over long distances has seen some progresses, while the distribution of multipartite entanglement over long distances remains unsolved. Here we report a two-dimensional quantum repeater protocol for the generation of multipartite entanglement over long distances with all-photonic framework to fill this gap. The yield of the proposed protocol shows long transmission distance under various numbers of network users. With the improved efficiency and flexibility of extending the number of users, we anticipate that our protocol can work as a significant building block for quantum networks in the future.