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Measuring quantum states provides a means to generate genuine random numbers. It has been shown that genuine randomness can be obtained even with an uncharacterized source by measuring two incompatible bases [Phys. Rev. X 6, 011020 (2016)]. As coherence is the necessary source for generating randomness, we extend the scheme and propose a framework for quantum random number generation with general uncharacterized coherence resource. The previous scheme can be treated as a special case under the framework by considering a nonlinear uncertainty-relation-based coherence witness. Considering general coherence witnesses, we propose a source-independent random-number generation scheme that achieves a higher randomness generation rate. Our paper highlights the close relation between coherence and random-number generation and may shed light on designing general semi-device-independent quantum information processing protocols.

Entanglement, the essential resource in quantum information processing, should be witnessed in many tasks such as quantum computing and quantum communication. The conventional entanglement witness method, relying on an idealized implementation of measurements, could wrongly conclude a separable state to be entangled due to imperfect detections. Inspired by the idea of a time-shift attack, we construct an attack on the conventional entanglement witness process and demonstrate that a separable state can be falsely identified to be entangled. To close such detection loopholes, based on a recently proposed measurement-device-independent entanglement witness method, we design and experimentally demonstrate a measurement-device-independent entanglement witness for a variety of two-qubit states. By the new scheme, we show that an entanglement witness can be realized without detection loopholes.

Quantum key distribution allows remote parties to generate information-theoretic secure keys. The bottleneck throttling its real-life applications lies in the limited communication distance and key generation speed, due to the fact that the information carrier can be easily lost in the channel. For all the current implementations, the key rate is bounded by the channel transmission probability $\eta$. Rather surprisingly, by matching the phases of two coherent states and encoding the key information into the common phase, this linear key-rate constraint can be overcome—the secure key rate scales with the square root of the transmission probability $O(\sqrt{\eta })$, as proposed in twin-field quantum key distribution [M. Lucamarini et al. Overcoming the Rate–Distance Limit of Quantum Key Distribution without Quantum Repeaters, Nature (London) 557, 400 (2018)]. To achieve this, we develop an optical-mode-based security proof that is different from the conventional qubit-based security proofs. Furthermore, the proposed scheme is measurement device independent; i.e., it is immune to all possible detection attacks. The simulation result shows that the key rate can even exceed the transmission probability $\eta$ between two communication parties. In addition, we apply phase postcompensation to devise a practical version of the scheme without phase locking, which makes the proposed scheme feasible with the current technology. This means that quantum key distribution can enjoy both sides of the world—practicality and security.

Random numbers are indispensable for a variety of applications ranging from testing physics foundations to information encryption. In particular, nonlocality test provide strong evidence for our current understanding of nature—quantum mechanics. All the random number generators (RNGs) used for the existing tests are constructed locally, making the test results vulnerable to the freedom-of-choice loophole. We report an experimental realization of RNGs based on the arrival time of cosmic photons. The measurement outcomes (raw data) pass the standard NIST statistical test suite. We present a realistic design to employ these RNGs in a Bell test experiment, which addresses the freedom-of-choice loophole.

Quantum mechanics provides the means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a manner that is independent of implementation devices. Here, we present an experimental study of device-independent quantum random number generation based on a detection-loophole-free Bell test with entangled photons. In the randomness analysis, without the independent identical distribution assumption, we consider the worst case scenario that the adversary launches the most powerful attacks against the quantum adversary. After considering statistical fluctuations and applying an $80\mathrm{Gb}\times 45.6\mathrm{Mb}$ Toeplitz matrix hashing, we achieve a final random bit rate of $114\mathrm{bits}/\mathrm{s}$, with a failure probability less than ${10}^{-5}$. This marks a critical step towards realistic applications in cryptography and fundamental physics tests.

Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. Due to the imperfection of measurement devices, a conventional coherence witness may lead to fallacious results. We show that the conventional witness could mistake an incoherent state as a state with coherence due to the inaccurate settings of measurement bases. In order to make the witness result reliable, we propose a measurement-device-independent coherence witness scheme without any assumptions on the measurement settings. We introduce the decoy-state method to significantly increase the capability of recognizing states with coherence. Furthermore, we experimentally demonstrate the scheme in a time-bin encoding optical system.

The generation and verification of large-scale entanglement are essential to the development of quantum technologies. In this paper, we present an efficient scheme to generate genuine multipartite entanglement of a large number of qubits by using the Heisenberg interaction. This method can be conveniently implemented in various physical platforms, including superconducting, trapped-ion, and cold-atom systems. In order to characterize the entanglement of the output quantum state, we generalize the stabilizer formalism and develop an entanglement witness method. In particular, we design a generic searching algorithm to optimize entanglement witness with a minimal number of measurement settings under a given noise level. From the perspective of practical applications, we numerically study the trade-off between the experiment efficiency and the detection robustness.

In the past two decades, quantum key distribution networks based on telecom fibers have been implemented on metropolitan and intercity scales. One of the bottlenecks lies in the exponential decay of the key rate with respect to the transmission distance. Recently proposed schemes mainly focus on achieving longer distances by creating a long-arm single-photon interferometer over two communication parties. Despite their advantageous performance over long communication distances, the requirement of phase locking between two remote lasers is technically challenging. By adopting the recently proposed mode-pairing idea, we realize high-performance quantum key distribution without global phase locking. Using two independent off-the-shelf lasers, we show a quadratic key-rate improvement over the conventional measurement-device-independent schemes in the regime of metropolitan and intercity distances. For longer distances, we also boost the key rate performance by 3 orders of magnitude via 304 km commercial fiber and 407 km ultralow-loss fiber. We expect this ready-to-implement high-performance scheme to be widely used in future intercity quantum communication networks.

By simulating four quantum key distribution (QKD) experiments and analyzing one decoy-state QKD experiment, we compare two data postprocessing schemes based on security against individual attack by Lütkenhaus, and unconditional security analysis by Gottesman-Lo-Lütkenhaus-Preskill. Our results show that these two schemes yield close performances. In QKD, since unconditional security is highly sought after, we conclude that one is better off considering unconditional security, rather than restricting to individual attacks.

Quantum key distribution provides information-theoretically-secure communication. In practice, device imperfections may jeopardise the system security. Device-independent quantum key distribution solves this problem by providing secure keys even when the quantum devices are untrusted and uncharacterized. Following a recent security proof of the device-independent quantum key distribution, we improve the key rate by tightening the parameter choice in the security proof. In practice where the system is lossy, we further improve the key rate by taking into account the loss position information. From our numerical simulation, our method can outperform existing results. Meanwhile, we outline clear experimental requirements for implementing device-independent quantum key distribution. The maximal tolerable error rate is 1.6%, the minimal required transmittance is 97.3%, and the minimal required visibility is $96.8\%$.

The Clauser-Horne-Shimony-Holt inequality test is widely used as a means of invalidating the local deterministic theories and a tool of device-independent quantum cryptographic tasks. There exists a randomness (free will) loophole in the test, which is widely believed impossible to be closed perfectly, that is, certain random inputs are required for the test. Following a randomness quantification method used in literature, we investigate the randomness required in the test under various assumptions. By comparing the results, we conclude that, in order to make the test result reliable, it is more important to rule out the correlation between multiple runs than the correlation between two parties.

A Bell test can rule out local realistic models and has potential applications in communication and information tasks. For example, a Bell's inequality violation can certify the presence of intrinsic randomness in measurement outcomes, which can be used to generate unpredictable random numbers. Nevertheless, a Bell test requires measurements that are chosen independently of environment in the test, as would be the case if the measurement setting choices were themselves intrinsically random. Such situation seems to create a “bootstrapping problem” recently addressed in the BIG Bell Test, a collection of various Bell tests using human choices. Here, we report in detail our experimental methods and results within the BIG Bell Test, specifically for a special type of Bell inequality, known as the measurement-dependent local inequality. With this inequality, even a small amount of measurement independence makes it possible to disprove local realistic models. The experiment utilizes human-generated random numbers in selecting the measurement settings and is implemented with space-like separation between two distant measurement sites. The experimental result violates a Bell's inequality, which cannot be explained by local hidden variable models with independence parameter (as defined in [G. Pütz et al., Phys. Rev. Lett. 113, 190402 (2014)]) $l>0.10\pm 0.05$. This result further quantifies the degree to which a local hidden variable model would need to constrain human choices, if it is to reproduce the experimental results.

Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constraints on the accuracy of two noncommuting observables. The existing uncertainty relations adopt variance or entropic measures, which are functions of observed outcome distributions, to quantify the uncertainty. According to recent studies of quantum coherence, such uncertainty measures contain both classical (predictable) and quantum (unpredictable) components. In order to extract out the quantum effects, we define quantum uncertainty to be the coherence of the state on the measurement basis. We discover a quantum uncertainty relation using coherence between two measurement noncommuting bases. Furthermore, we analytically derive the quantum uncertainty relation for the qubit case with three widely adopted coherence measures, the relative entropy of coherence, the coherence of formation, and the $l_1$ norm of coherence.

Quantum digital signatures (QDSs) provide a means for signing electronic communications with information-theoretic security. However, all previous demonstrations of quantum digital signatures assume trusted measurement devices. This renders them vulnerable against detector side-channel attacks, just like quantum key distribution. Here we exploit a measurement-device-independent (MDI) quantum network, over a metropolitan area, to perform a field test of a three-party MDI QDS scheme that is secure against any detector side-channel attack. In so doing, we are able to successfully sign a binary message with a security level of about ${10}^{-7}$. Remarkably, our work demonstrates the feasibility of MDI QDSs for practical applications.

The randomness from a quantum random-number generator (QRNG) relies on the accurate characterization of its devices. However, device imperfections and inaccurate characterizations can result in wrong entropy estimation and bias in practice, which highly affects the genuine randomness generation and may even induce the disappearance of quantum randomness in an extreme case. Here we experimentally demonstrate a measurement-device-independent (MDI) QRNG based on time-bin encoding to achieve certified quantum randomness even when the measurement devices are uncharacterized and untrusted. The MDI-QRNG is randomly switched between the regular randomness generation mode and a test mode, in which four quantum states are randomly prepared to perform measurement tomography in real time. With a clock rate of 25 MHz, the MDI-QRNG generates a final random bit rate of 5.7 kbps. Such implementation with an all-fiber setup provides an approach to construct a fully integrated MDI-QRNG with trusted but error-prone devices in practice.

In quantum key distribution (QKD), the bit error rate is used to estimate the information leakage and hence determines the amount of privacy amplification—making the final key private by shortening the key. In general, there exists a threshold of the error rate for each scheme, above which no secure key can be generated. This threshold puts a restriction on the environment noises. For example, a widely used QKD protocol, the Bennett-Brassard protocol, cannot tolerate error rates beyond 25%. A new protocol, round-robin differential phase-shifted (RRDPS) QKD, essentially removes this restriction and can in principle tolerate more environment disturbance. Here, we propose and experimentally demonstrate a passive RRDPS QKD scheme. In particular, our 500 MHz passive RRDPS QKD system is able to generate a secure key over 50 km with a bit error rate as high as 29%. This scheme should find its applications in noisy environment conditions.

Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a specific (classical) computational basis. Recently, by regarding coherence as a physical resource, Baumgratz et al. [Phys. Rev. Lett. 113, 140401 (2014)] presented a comprehensive framework for coherence measures. Here, we propose a quantum coherence measure essentially using the intrinsic randomness of measurement. The proposed coherence measure provides an answer to the open question in completing the resource theory of coherence. Meanwhile, we show that the coherence distillation process can be treated as quantum extraction, which can be regarded as an equivalent process of classical random number extraction. From this viewpoint, the proposed coherence measure also clarifies the operational aspect of quantum coherence. Finally, our results indicate a strong similarity between two types of quantumness—coherence and entanglement.

Decoy states have been proven to be a very useful method for significantly enhancing the performance of quantum key distribution systems with practical light sources. Although active modulation of the intensity of the laser pulses is an effective way of preparing decoy states in principle, in practice passive preparation might be desirable in some scenarios. Typical passive schemes involve parametric down-conversion. More recently, it has been shown that phase-randomized weak coherent pulses (WCP) can also be used for the same purpose [M. Curty et al., Opt. Lett. 34, 3238 (2009).] This proposal requires only linear optics together with a simple threshold photon detector, which shows the practical feasibility of the method. Most importantly, the resulting secret key rate is comparable to the one delivered by an active decoy-state setup with an infinite number of decoy settings. In this article we extend these results, now showing specifically the analysis for other practical scenarios with different light sources and photodetectors. In particular, we consider sources emitting thermal states, phase-randomized WCP, and strong coherent light in combination with several types of photodetectors, like, for instance, threshold photon detectors, photon number resolving detectors, and classical photodetectors. Our analysis includes as well the effect that detection inefficiencies and noise in the form of dark counts shown by current threshold detectors might have on the final secret key rate. Moreover, we provide estimations on the effects that statistical fluctuations due to a finite data size can have in practical implementations.

Nonlocality, evidenced by the violation of Bell inequalities, not only signifies entanglement but also highlights measurement incompatibility in quantum systems. Utilizing the tilted Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, our high-efficiency optical setup achieves a loophole-free violation of $2.0132$. This result provides a device-independent lower bound on entanglement, quantified as the entanglement of formation at $0.0159$. Moreover, by tuning the parameters of the tilted CHSH inequality, we enhance the estimation of measurement incompatibility, which is quantified by an effective overlap of $4.3883\times {10}^{-5}$. To explore the intricate interplay among nonlocality, entanglement, and measurement incompatibility, we generate mixed states, allowing for flexible modulation of entanglement via fast switching among the four Bell states using Pockels cells, achieving a fidelity above $99.10\%$. Intriguingly, our results reveal a counterintuitive relationship where increasing incompatibility initially boosts nonlocality but eventually leads to its reduction. Typically, maximal nonlocality does not coincide with maximal incompatibility. This experimental study sheds light on the optimal management of quantum resources for Bell-inequality-based quantum information processing.

In principle, quantum key distribution (QKD) offers information-theoretic security based on the laws of physics. In practice, however, the imperfections of realistic devices might introduce deviations from the idealized models used in security analyses. Can quantum code breakers successfully hack real systems by exploiting the side channels? Can quantum code makers design innovative countermeasures to foil quantum code breakers? Theoretical and experimental progress in the practical security aspects of quantum code making and quantum code breaking is reviewed. After numerous attempts, researchers now thoroughly understand and are able to manage the practical imperfections. Recent advances, such as the measurement-device-independent protocol, have closed critical side channels in the physical implementations, paving the way for secure QKD with realistic devices.