Chip-based photonic graph states

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

We present theoretical and experimental advances on photon-pair generation through spontaneous parametric down-conversion (SPDC) in nonlinear nanostructures and metasurfaces, underpinning quantum entanglement engineering at sub-wavelength scale for photon shaping with tailored polarization and spatial correlations. We derive explicit theoretical expressions for the measurable photon counts and quantum correlations, incorporating material dispersion and absorption characteristics [Phys. Rev. Lett. 117, 123901 (2016)], and demonstrate experimentally the generation of quantum heralded photon pairs from a single AlGaAs nanodisk [Optica 6, 1416 (2019)]. We further reveal the opportunities to enhance the generation rate through high-Q resonances including bound states in the continuum [doi:10.1117/12.2539888 (2019)]. We also outline the applications of metasurfaces for the manipulation and measurement of multi-photon quantum states for free-space quantum imaging and communications.

Encoding and processing quantum information in the time-of-arrival of photons offer significant advantages for quantum information science and technology. These advantages include ease of experimental realization, robustness over photon state transmission, and compatibility with existing telecommunication infrastructure. Additionally, time-of-arrival encoding has the potential for high-rate quantum communication and holds promise for the future development of quantum internet. This review explores the generation, processing, and applications of time-encoded quantum states, focusing on both single-photon states, energy–time entanglement, and time-bin entanglement. We summarize the nonlinear optics platforms and advanced laser and modulation techniques utilized for photon sources that enable quantum information encoding onto the photons' time-of-arrival. We also highlight advanced quantum state processing methods in the time domain, including the Franson interferometry, optical switch-based schemes, and state-of-the-art measurement and detection schemes that allow for high-speed and multi-dimensional quantum operations. Finally, we review the mainstream implementations mainly including the quantum communication demonstrations and outline future directions for developing practical quantum networks leveraging time-encoded photon states.

Single molecular systems are typical quantum confinement systems, which have rich electronic states, photon states and spin states due to their discrete energy levels, localized orbitals and diverse chemical structures. The states determined by quantum mechanics in these molecular systems make it possible to serve as great physical entities for future quantum information technology. The detection and manipulation of quantum states on a single molecule scale are beneficial to the bottom-up construction of quantum devices. Owing to the highly limited spatial localization of single molecular systems, it is difficult to accurately address and manipulate them with conventional macroscopic characterization methods. Scanning tunneling microscope (STM) is such a powerful tool that it can achieve high-resolution real-space imaging as well as spectroscopic investigation, with the ability to <i>in-situ</i> manipulating the individual atoms or molecules. It can also work jointly with various near-field or external field characterization techniques, making it a most important technique for precisely detecting and manipulating quantum properties at a single molecule level. In this paper, we review recent research progress of quantum states of surface-supported single molecules and relevant structures based on scanning tunneling microscopy. We start from the methods for the synthesis of molecular structures with desired quantum states, and then we review the recent advances in the local spin states for single molecular systems and the optical properties of single molecules serving as a single-photon source. An emerging family of molecular nanographene systems showing intriguing topological properties and magnetic properties is also reviewed. In the last part, we summarize the research progress made recently and prospect the future development of the quantum states at a single molecular level.

Hybrid quantum circuits combining advantages of each individual system have provided a promising platform for quantum information processing. Here we propose an experimental scheme to directly couple a transmon qubit to an individual spin in the nitrogen-vacancy (NV) center, with a coupling strength three orders of magnitude larger than that for a single spin coupled to a microwave cavity. This direct coupling between the transmon and the NV center could be utilized to make a transmon bus, leading to a coherently virtual exchange among different single spins. Furthermore, we demonstrate that, by coupling a transmon to a low-density NV ensemble, a SWAP operation between the transmon and NV ensemble is feasible and a quantum non-demolition measurement on the state of NV ensemble can be realized on the cavity-transmon-NV-ensemble hybrid system. Moreover, on this system, a virtual coupling can be achieved between the cavity and NV ensemble, which is much larger in magnitude than the direct coupling between the cavity and the NV ensemble. The photon state in cavity can be thus stored into NV spins more efficiently through this virtual coupling.

Metasurfaces based on resonant nanophotonic structures have enabled innovative types of flat-optics devices that often outperform the capabilities of bulk components, yet these advances remain largely unexplored for quantum applications. We show that nonclassical multiphoton interferences can be achieved at the subwavelength scale in all-dielectric metasurfaces. We simultaneously image multiple projections of quantum states with a single metasurface, enabling a robust reconstruction of amplitude, phase, coherence, and entanglement of multiphoton polarization-encoded states. One- and two-photon states are reconstructed through nonlocal photon correlation measurements with polarization-insensitive click detectors positioned after the metasurface, and the scalability to higher photon numbers is established theoretically. Our work illustrates the feasibility of ultrathin quantum metadevices for the manipulation and measurement of multiphoton quantum states, with applications in free-space quantum imaging and communications.

Taking advantage of quantum mechanics for executing computational tasks faster than classical computers1 or performing measurements with precision exceeding the classical limit2,3 requires the generation of specific large and complex quantum states. In this context, cluster states4 are particularly interesting because they can enable the realization of universal quantum computers by means of a ‘one-way’ scheme5, where processing is performed through measurements6. The generation of cluster states based on sub-systems that have more than two dimensions, d-level cluster states, provides increased quantum resources while keeping the number of parties constant7, and also enables novel algorithms8. Here, we experimentally realize, characterize and test the noise sensitivity of three-level, four-partite cluster states formed by two photons in the time9 and frequency10 domain, confirming genuine multi-partite entanglement with higher noise robustness compared to conventional two-level cluster states6,11–13. We perform proof-of-concept high-dimensional one-way quantum operations, where the cluster states are transformed into orthogonal, maximally entangled d-level two-partite states by means of projection measurements. Our scalable approach is based on integrated photonic chips9,10 and optical fibre communication components, thus achieving new and deterministic functionalities. The creation and manipulation of large quantum states is necessary for quantum information processing tasks. Three-level, four-partite cluster states have now been created in the time and frequency domain of two photons on-chip.

We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atom-like qubit and those of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.

In a quantum network, transmission of quantum states is performed by photonic channels, which distribute them between remote locations. However, the storage and manipulation of the photons is more problematic. Recently, several schemes have been proposed to store photons efficiently by interfacing the photonic channel with an atomic system, i.e. an atomic ensemble. In those schemes, the photonic input state is transferred to a collective atomic state. But the manipulation of photonic states requires the ability to perform entangling operations. We show how to do this manipulation and perform a deterministic entangling gate between photons. To this order, we interface a system of cold neutral atoms in an optical lattice with the photonic channel, such that now the atoms are not only used to store information, but also to process it by means of cold controlled collisions in the lattice.

We present a programmable silicon photonic four-qubit integrated circuit for the generation and manipulation of diverse quantum states. The silicon photonic chip integrates photon-pair sources, pump-reducing filters, wavelength-division-multiplexing filters, Mach–Zehnder interferometer switches, and single-qubit arbitrary gates, enabling versatile state preparation and tomography. We measure Hong–Ou–Mandel interference with an impressive 98% visibility using four-photon coincidence, laying the foundation for high-purity qubits. Our analysis involves estimating the fidelity and purity of distinct quantum states through maximum-likelihood estimation applied to tomographic measurements. In our experimental results, we showcase the following achievements: a heralded single qubit achieving 98.2% fidelity and 98.3% purity, a Bell state reaching 95.2% fidelity and 94.8% purity, and a four-qubit system with two simultaneous Bell states exhibiting 87.4% fidelity and 84.6% purity. Finally, a four-qubit Greenberger–Horne–Zeilinger (GHZ) state demonstrates 85.4% fidelity and 81.7% purity. In addition, we certify the entanglement of the four-photon GHZ state through Bell’s inequality violations and a negative entanglement witness.

Lithium niobate has emerged as a promising platform for integrated quantum optics, enabling efficient generation, manipulation, and detection of quantum states of light. However, integrating single-photon detectors requires cryogenic operating temperatures, since the best performing detectors are based on narrow superconducting wires. While previous studies have demonstrated the operation of quantum light sources and electro-optic modulators in LiNbO3 at cryogenic temperatures, the thermal transition between room temperature and cryogenic conditions introduces additional effects that can significantly influence device performance. In this paper, we investigate the generation of pyroelectric charges and their impact on the optical properties of lithium niobate waveguides when changing from room temperature to 25 K, and vice versa. We measure the generated pyroelectric charge flow and correlate this with fast changes in the birefringence acquired through the Sénarmont-method. Both electrical and optical influence of the pyroelectric effect occur predominantly at temperatures above 100 K.

Unidirectional photonic edge states arise at the interface between two topologically distinct photonic crystals. Here, we demonstrate a micrometer-scale GaAs photonic ring resonator, created using a spin Hall-type topological photonic crystal waveguide. Embedded InGaAs quantum dots are used to probe the mode structure of the device. We map the spatial profile of the resonator modes and demonstrate the control of the mode confinement through tuning of the photonic crystal lattice parameters. The intrinsic chirality of the edge states makes them of interest for applications in integrated quantum photonics, and the resonator represents an important building block toward the development of such devices with embedded quantum emitters.

Quantum secret sharing is an important way to achieve secure communications, which has critical applications in the field of information security for its physical properties. According to the perspective of the practical applications, improving the confidentiality and integrity of secret sharing schemes is a good method to increase the security and reliability of communications. In this paper, we propose a quantum secret sharing scheme based on generator matrix segmentation and the structural features of quantum graph states. The security of the secure secret sharing scheme is guaranteed by the pattern of transferring information by stabilizers, scalability of the information and new recovery strategy provided by the entanglement of the related graph states. It puts forward an effective solution to the problem of matrix cycle period, where some numbers without the primitive element cannot construct the generation matrix. First of all, the physical properties of quantum bits (qubits), such as uncertainty principle, no-cloning theorem and indistinguishability, not only optimize the classical schemes but also ensure the absolute safety of communication. Secondly, the application of matrix segmentation makes secret information has better scalability. It improves the coding diversity and the difficulty in deciphering. Thirdly, the favorable entanglement properties and mature experiment preparation techniques of graph states provide an approach to the practical applications. The superiority of the yielded graph states is described in graphical fashion with an elegant stabilizer. Fourthly, the shuffling operation can ensure the independence of the message among participants. Therefore, Eve can not obtain any useful information by measuring randomly. Two group-recovery protocols are proposed to show the secret recovering processing through rebuilding sub-secrets among legal cooperative participants. In the scheme design, the dealer extracts the classical secret information according to the corresponding principle between the classical and quantum information, and divides the classical secret through generated matrix which is produced with the primitive elements in finite domain satisfying the linear independence for any k column vectors. Then the dealer encodes information into graph states and distributes particles to the legal participants with unitary operations. Subsequently, the credible center obtains sub-secrets by the theory of graph states and the group recovery protocol. He can achieve the initial classical secret via the inverse algorithm of matrix segmentation. After getting the classical secret, he recovers quantum secret according to the relationship between classical information and quantum information. Theoretical analysis shows that this scheme can provide better security and scalability of the information. It is appropriate to realize the secret sharing in the quantum network communication to protect secrets from eavesdropping. Also, it can provide an approach to designing diverse and scalable quantum secure communication schemes based on quantum graph states, the algorithm of matrix segmentation, and group-recovery protocol.

Quantum science and technology have seen rapid progress in recent decades, finding applications in computation, information processing, communication, and sensing. Accurate characterization and manipulation of quantum states is essential to the successful implementation of these applications. Moreover, optimal quantum state estimation is closely related to fundamental questions, such as limits on how fast information can be extracted about quantum systems. In this thesis, we present several contributions to efficiently estimating and transforming quantum states. We discuss optimal quantum state estimation, both in the regime of few available quantum systems as well as the asymptotic regime. We numerically investigate how assuming a pure-state can affect the performance of tomographic methods, and where adaptive quantum state tomography is in fact advantageous. While collective measurements have been formally considered as optimal solutions to various problems in quantum information, their implementation has been largely neglected due to experimental challenges. We present a proof-of-concept experiment realizing Massar and Popescu's optimal collective measurement for quantum state estimation, utilizing two-photon interference and polarization-dependent loss to achieve non-maximally entangled state projections. We demonstrate that collective strategies can outperform the best separable measurements. Furthermore, we introduce and experimentally implement a fast and automated optical polarization compensation scheme using liquid crystal variable retarders and rotating quarter-wave plate tomography. Desired accuracy thresholds can be achieved within a few compensation steps. Finally, we use a matrix-model approach to investigate the realization of spatial unitary transformations via sequences of thin phase gratings and free-space propagation. We numerically demonstrate that the grating parameters and propagation distances can be optimized to achieve various two-beam and three-beam unitary transformations, such as Pauli gates and the discrete Fourier transform. Through experimental and numerical approaches, this thesis offers new perspectives on methods for quantum state estimation and unitary transformation.

Large-scale quantum silicon photonic devices can represent a viable route to the generation of large entangled quantum states (graph states)[1], exploiting the generation of multiple pairs of photons on chip. Graph state applications are diverse, spanning from measurement-based quantum computing to quantum error correction and quantum communication [2]. Silicon photonics represents a promising platform for its stability, reconfigurability, high-density and high-performance optical components.