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Non-Abelian anyons, which correspond to collective excitations possessing multiple fusion channels and noncommuting braiding statistics, serve as the fundamental constituents for topological quantum computation. Here, we reveal the exotic Bloch oscillations (BOs) induced by non-Abelian fusion of Fibonacci anyons. It is shown that the interplay between fusion-dependent internal energy levels and external forces can induce BOs and Bloch-Zener oscillations (BZOs) of coupled fusion degrees with varying periods. In this case, the golden ratio of the fusion matrix can be determined by the period of BOs or BZOs in conjunction with external forces, giving rise to an effective way to unravel non-Abelian fusion. Furthermore, we experimentally simulate nonAbelian fusion BOs by mapping Schrodinger equation of two Fibonacci anyons onto dynamical equation of electric circuits. Through the measurement of impedance spectra and voltage evolution, both fusion-dependent BZOs and BOs are simulated. Our findings establish a connection between BOs and non-Abelian fusion, providing a versatile platform for simulating numerous intriguing phenomena associated with non-Abelian physics.

This review offers a comprehensive exploration and synthesis of recent advancements in the domain of quantum correlation sharing facilitated through sequential measurements. We initiate our inquiry by delving into the interpretation of the joint probability, laying the foundation for an examination of quantum correlations within the context of specific measurement methods. The subsequent section meticulously explores nonlocal sharing under diverse measurement strategies and scenarios, with a specific focus on investigating the impact of these strategies on the dissemination of quantum nonlocality. Key perspectives such as "asymmetry" and "weak value" are scrutinized through detailed analyses across various scenarios, allowing us to evaluate the potential of nonlocality sharing. We also provide a retrospective overview of experimental endeavors associated with this phenomenon. The third part of our exploration presents research findings on steering sharing, offering clarity on the feasibility of steering sharing and summarizing the distinctive properties of quantum steering sharing in different scenarios. Continuing our journey, the fourth section delves into discussions on the sharing of diverse quantum correlations, encompassing network nonlocality, quantum entanglement, and quantum contextuality. Moving forward, the fifth section conducts a comprehensive review of the progress in the application of quantum correlation sharing, specifically based on sequential measurement strategies. Applications such as quantum random access coding, random number generation, and self-testing tasks are highlighted. Finally, we discuss and list some of the key unresolved issues in this research field, and conclude the entire article.

Qudits with a large Hilbert space to host quantum information are widely utilized in various applications, such as quantum simulation and quantum computation, but the manipulation and scalability of qudits still face challenges. Here, we propose a scheme to directly and locally transfer quantum information from multiple atomic qubits to a single qudit and vice versa in an optical cavity. With the qubit-qudit interaction, our scheme can transfer quantum states efficiently and measurement-independently. In addition, this scheme can be extended to the non-local case, where a high-dimensional maximal entangled state with asymmetric particle numbers can be robustly generated for realizing long-distance quantum communication. Such an information interface for qubits and qudit may have enlightening significance for future research on quantum systems in hybrid dimensions., Comment: 12 pages, 5 figures

Flat-band topologies and localizations in non-interacting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in interacting systems has aroused great interest. In particular, it is theoretically shown that the strong-interaction could drive the formation of nontrivial topological flat bands, even dispersive trivial bands dominate the single-particle counterparts. However, the experimental observation of those interesting phenomena is still lacking. Here, we experimentally simulate the interaction-induced flat-band localizations and topological edge states in electrical circuit networks. We directly map the eigenstates of two correlated bosons in one-dimensional Aharonov Bohm cages to modes of two-dimensional circuit lattices.In this case, the two-boson flat-bands and topological edge states are detected by measuring frequency-dependent impedance responses and voltage dynamics in the time domain. Our finding suggests a flexible platform to simulate the interaction-induced flat-band topology, and may possess potential applications in designing novel electronic devices.

Quantum entanglement is a fundamental resource for quantum information processing and is widely used in quantum communication, quantum computation and quantum metrology. Early research on quantum entanglement mainly focus on qubit states, but in recent years, more and more research has begun to focus on high-dimensional entangled states. Compared with qubit entangled states, higher-dimensional entangled states have a larger information capacity and the potential to realize more complex quantum applications. In this Letter, we have experimentally prepared a special high-dimensional entangled state, the so-called three-photon asymmetric maximally entangled state, which consists of two two-dimensional photons and one four-dimensional photon. Using this asymmetric maximally entangled state as a resource, we have also implemented a proof-of-principle quantum teleportation experiment, realizing the transfer of quantum information from two qubits to a single ququart. The fidelities of the quantum teleportation range from 0.79 to 0.86, which are well above both the optimal single-copy ququart state-estimation limit of 2/5 and maximal qutrit-ququart overlap of 3/4, thus confirming a genuine and nonclassical four-dimensional teleportation. The asymmetric entangled state realized here has the potential to be used as a quantum interface in future quantum networks, allowing quantum information transfer between quantum objects of different dimensions via the quantum teleportation protocol demonstrated in this work., Comment: 6 pages, 2 figures

The prepare-and-measure theory is a new type of quantum paradox that reveals the incompatibility between classical theory and quantum mechanics in terms of the dimensionality of physical systems.Just as the Horodecki criterion can determine whether given quantum states are capable of exhibiting Bell nonclassicality, a similar criterion is needed for the prepare-and-measure theory to determine whether given uantum states can exhibit the prepare-and-measure nonclassicality. Recently, Poderini et al. [Phys. Rev. Research 2, 043106 (2020)] presented such a criterion for the prepare-and-measure nonclassicality. In this work, we experimentally validate this criterion -- 52 different sets of quantum states are prepared and tested one by one using this criterion to determine whether they can exhibit the prepare-and-measure nonclassicality, and the experimental results are in good agreement with the theoretical expectations. The criterion experimentally verified here has the potential to be widely used in future research on the prepare-and-measure nonclassicality.

With high integration density and excellent optical properties, silicon photonics is becoming a promising platform for complete integration and large-scale optical quantum information processing. Scalable quantum information applications need photon generation and detection to be integrated on the same chip, and we have seen that various devices on the silicon photonic chip have been developed for this goal. This paper reviews the relevant research results and state-of-the-art technologies on the silicon photonic chip for scalable quantum applications. Despite the shortcomings, properties of some components have already met the requirements for further expansion. Furthermore, we point out the challenges ahead and further research directions for on-chip scalable quantum information applications.

To employ a quantum device, the performance of the quantum gates in the device needs to be evaluated first. Since the dimensionality of a quantum gate grows exponentially with the number of qubits, evaluating the performance of a quantum gate is a challenging task. Recently, a scheme called quantum gate verification (QGV) has been proposed, which can verifies quantum gates with near-optimal efficiency. In this paper, we implement a proof-of-principle optical experiment to demonstrate this QGV scheme. We show that for a single-qubit quantum gate, only $\sim300$ samples are needed to confirm the fidelity of the quantum gate to be at least $97\%$ with a $99\%$ confidence level using the QGV method, whereas, at least $\sim3000$ samples are needed to achieve the same result using the standard quantum process tomography method. The QGV method validated by this paper has the potential to be widely used for the evaluation of quantum devices in various quantum information applications.

Non-locality sharing for a three-qubit system via multilateral sequential measurements was deeply discussed. Different from 2-qubit case, it is shown that non-locality sharing between $\mathrm{Alice_{1}-Bob_{1}-Charlie_{1}}$ and $\mathrm{Alice_{2}-Bob_{2}-Charlie_{2}}$ in 3-qubit system can be observed, where two Mermin-Ardehali-Belinskii-Klyshko (MABK) inequalities can be violated simultaneously. What's more, a complete non-locality sharing with 8 MABK inequalities violations simultaneously can be also observed. Compared with 2-qubit case, the nonlocal sharing in a three qubit system shows more novel characteristics.

In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets expectations. In this Letter, we propose a new approach solving this problem using machine-learning techniques. Compared to other fidelity estimation methods, our method is applicable to arbitrary quantum states, the number of required measurement settings is small, and this number does not increase with the size of the system. For example, for a general five-qubit quantum state, only four measurement settings are required to predict its fidelity with $\pm1\%$ precision in a nonadversarial scenario. This machine-learning-based approach for estimating quantum state fidelity has the potential to be widely used in the field of quantum information., Comment: 20 pages, 10 figures

A direct measurement protocol allows reconstructing specific elements of the density matrix of a quantum state without using quantum state tomography. However, the direct measurement protocols to date are primarily based on weak or strong measurements with an ancillary pointer, which interacts with the investigated system to extract information about the specified elements. Here, we present a direct measurement scheme based on phase-shifting operations which do not need ancillary pointers. In this method, estimates of at most six expectation values of projective observables suffice to determine any specific element of an unknown quantum density matrix. A concrete quantum circuit to implement this direct measurement protocol for multiqubit states is provided, which is composed of just single-qubit gates and two multiqubit controlled-phase gates. This scheme is also extended for the direct measurement of the density matrix of continuous-variable quantum states. Our method can be used in quantum information applications where only partial information about the quantum state needs to be extracted, for example, problems such as entanglement witnessing, fidelity estimation of quantum systems, and quantum coherence estimation., Comment: 6 pages, 5 figures

Quantum mechanics provides a disembodied way to transfer quantum information from one quantum object to another. In theory, this quantum information transfer can occur between quantum objects of any dimension, yet the reported experiments of quantum information transfer to date have mainly focused on the cases where the quantum objects have the same dimension. Here we theoretically propose and experimentally demonstrate a scheme for quantum information transfer between quantum objects of different dimensions.By using an optical qubit-ququart entangling gate, we observe the transfer of quantum information between two photons with different dimensions, including the flow of quantum information from a four-dimensional photon to a two-dimensional photon and vice versa.The fidelities of the quantum information transfer range from 0.700 to 0.917, all above the classical limit of 2/3. Our work sheds light on a new direction for quantum information transfer and demonstrates our ability to implement entangling operations beyond two-level quantum systems., Comment: 12 pages, 10 figures

Undoing a unitary operation, $i.e$. reversing its action, is the task of canceling the effects of a unitary evolution on a quantum system, and it may be easily achieved when the unitary is known. Given a unitary operation without any specific description, however, it is a hard and challenging task to realize the inverse operation. Recently, a universal quantum circuit has been proposed [Phys.Rev.Lett. 123, 210502 (2019)] to undo an arbitrary unknown $d$-dimensional unitary $U$ by implementing its inverse with a certain probability. In this letter, we report the experimental reversing of three single-qubit unitaries $(d = 2)$ by linear optical elements. The experimental results prove the feasibility of the reversing scheme, showing that the average fidelity of inverse unitaries is $F=0.9767\pm0.0048$, in close agreement with the theoretical prediction., Comment: 5 pages, 3figures

Integrated photonics has the advantages of miniaturization, low cost, and CMOS compatibility, and it provides a stable, highly integrated, and practical platform for quantum key distribution (QKD). While photonic integration of optical components has greatly reduced the overall cost of QKD systems, single-photon detectors (SPDs) have become the most expensive part of a practical QKD system. In order to circumvent this obstacle and make full use of SPDs, we have designed and fabricated a QKD receiver chip for multiple users. Our chip is based on a time-division multiplexing technique and makes use of a single set of SPDs to support up to four users' QKD. Our proof-of-principle chip-based QKD system is capable of producing an average secret key rate of 13.68 kbps for four users with a quantum bit error rate (QBER) as low as 0.51% over a simulated distance of 20 km in fiber. Our result clearly demonstrates the feasibility of multiplexing SPDs for setting QKD channels with different users using photonic integrated chip and may find applications in the commercialization of quantum communication technology.

A well-known property of quantum nonlocality is monogamy. However, recent research by Silva \emph{et al.} shows that multiple observers can share the nonlocality by using weak measurements [Phys. Rev. Lett. 114, 250401 (2015)]. There is an open question left in their result: whether the nonlocality of a single particle from an entangled pair can be shared among more than two observers that act sequentially and independently of each other? In this work, we analytical and numerical shows that it is possible to observe a triple violation of CHSH inequality between Alice and three Bobs when the measurements of each of the several observers at one side are unbiased with respect to the previous observers. This result overturns the conclusions and proofs of previous related work on this issue which has been widely shared in the scientific community before., Comment: The result of the violation between Alice and the third Bobs is obtained in bias case, but not the unbias case

The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it amenable to an experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is more friendly for experimental implementation, i.e., one may only measure the observables in $x$-, $y$-, or $z$-axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with the theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states., Comment: 12 pages,8 figures

Nonlocality plays a fundamental role in quantum information science. Recently, it has been theoretically predicted and experimentally demonstrated that the nonlocality of an entangled pair may be shared among multiple observers using weak measurements with moderate strength. Here we devise an optimal protocol of nonlocality sharing among three observers and show experimentally that nonlocality sharing may be also achieved using weak measurements with near-maximum strength. Our result sheds light on the interplay between nonlocality and quantum measurements and, may find applications in quantum steering, unbounded randomness certification and quantum communication network., Comment: 6 pages, 4 figures

Exploiting semiconductor fabrication techniques, natural carriers of quantum information such as atoms, electrons, and photons can be embedded in scalable integrated devices. Integrated optics provides a versatile platform for large-scale quantum information processing and transceiving with photons. Scaling up the integrated devices for quantum applications requires highperformance single-photon generation and photonic qubit-qubit entangling operations. However, previous demonstrations report major challenges in producing multiple bright, pure and identical single-photons, and entangling multiple photonic qubits with high fidelity. Another notable challenge is to noiselessly interface multiphoton sources and multiqubit operators in a single device. Here we demonstrate on-chip genuine multipartite entanglement and quantum teleportation in silicon, by coherently controlling an integrated network of microresonator nonlinear single-photon sources and linear-optic multiqubit entangling circuits. The microresonators are engineered to locally enhance the nonlinearity, producing multiple frequencyuncorrelated and indistinguishable single-photons, without requiring any spectral filtering. The multiqubit states are processed in a programmable linear circuit facilitating Bell-projection and fusion operation in a measurement-based manner. We benchmark key functionalities, such as intra-/inter-chip teleportation of quantum states, and generation of four-photon Greenberger-HorneZeilinger entangled states. The production, control, and transceiving of states are all achieved in micrometer-scale silicon chips, fabricated by complementary metal-oxide-semiconductor processes. Our work lays the groundwork for scalable on-chip multiphoton technologies for quantum computing and communication.

Integrated optics is an engineering solution proposed for exquisite control of photonic quantum information. Here we use silicon photonics and the linear combination of quantum operators scheme to realise a fully programmable two-qubit quantum processor. The device is fabricated with readily available CMOS based processing and comprises four nonlinear photon-sources, four filters, eighty-two beam splitters and fifty-eight individually addressable phase shifters. To demonstrate performance, we programmed the device to implement ninety-eight various two-qubit unitary operations (with average quantum process fidelity of 93.2$\pm$4.5%), a two-qubit quantum approximate optimization algorithm and efficient simulation of Szegedy directed quantum walks. This fosters further use of the linear combination architecture with silicon photonics for future photonic quantum processors., Comment: 23 pages, 13 figures