Bell-state Measurement Research Articles

Entanglement Swapping and Quantum Correlations via Symmetric Joint Measurements.

We use hyperentanglement to experimentally realize deterministic entanglement swapping based on quantum elegant joint measurements. These are joint projections of two qubits onto highly symmetric, isoentangled bases. We report measurement fidelities no smaller than 97.4%. We showcase the applications of these measurements by using the entanglement swapping procedure to demonstrate quantum correlations in the form of proof-of-principle violations of both bilocal Bell inequalities and more stringent correlation criteria corresponding to full network nonlocality. Our results are a foray into entangled measurements and nonlocality beyond the paradigmatic Bell state measurement and they show the relevance of more general measurements in entanglement swapping scenarios.

Entangling single atoms over 33 km telecom fibre

Quantum networks promise to provide the infrastructure for many disruptive applications, such as efficient long-distance quantum communication and distributed quantum computing1,2. Central to these networks is the ability to distribute entanglement between distant nodes using photonic channels. Initially developed for quantum teleportation3,4 and loophole-free tests of Bell’s inequality5,6, recently, entanglement distribution has also been achieved over telecom fibres and analysed retrospectively7,8. Yet, to fully use entanglement over long-distance quantum network links it is mandatory to know it is available at the nodes before the entangled state decays. Here we demonstrate heralded entanglement between two independently trapped single rubidium atoms generated over fibre links with a length up to 33 km. For this, we generate atom–photon entanglement in two nodes located in buildings 400 m line-of-sight apart and to overcome high-attenuation losses in the fibres convert the photons to telecom wavelength using polarization-preserving quantum frequency conversion9. The long fibres guide the photons to a Bell-state measurement setup in which a successful photonic projection measurement heralds the entanglement of the atoms10. Our results show the feasibility of entanglement distribution over telecom fibre links useful, for example, for device-independent quantum key distribution11–13 and quantum repeater protocols. The presented work represents an important step towards the realization of large-scale quantum network links.

Measurement-based logical qubit entanglement purification

Entanglement purification is the distilling of high-quality entanglement from low-quality entanglement and is a key element in the quantum repeater. As a new branch of entanglement purification, the measurement-based entanglement purification protocol (MBEPP) only requires one to perform the Bell state measurement to couple resource states with noisy pairs, and it tolerates more local noise than the conventional purification protocols. Existing MBEPPs usually focus on physical qubit entanglement. In this paper, we propose a measurement-based logical qubit entanglement purification protocol (MBLEPP) with quantum nondemolition detection (QND), where the qubit is encoded in the quantum parity code. The results show that this MBLEPP can also work with photon loss under the conditions that each block of the logical Bell state measurement contains at least one physical qubit, that at least one of the blocks is intact, and that the entanglement exists between all blocks. Moreover, we also consider the MBLEPP with imperfect QND. We show that below a certain QND error threshold, this MBLEPP can still work. In this way, this MBLEPP not only obtains high-fidelity entanglement but also tolerates photon loss and the error from imperfect QND. This MBLEPP combines the benefits of the MBEPP and quantum error correction code and may have potential application in long-distance quantum communication.

Teleportation of discrete-variable qubits via continuous-variable lossy channels

The Continuous-Variable (CV) quantum state of light allows for the teleportation of a Discrete-Variable (DV) photonic qubit. Such an operation is useful in the realm of hybrid quantum networks. However, it is known that the teleportation of a DV qubit via a Gaussian CV resource channel is severely limited under channel loss, with a teleportation fidelity beyond the classical limit unattainable for losses exceeding a small threshold of 0.5 dB. In this work, we present a new non-deterministic teleportation protocol that combines a Gaussian CV resource channel with a modified form of the Bell State Measurement that accommodates a DV-qubit fidelity beyond the classical limit for channel losses up to 20~dB. Beyond this orders of magnitude improvement, we also show how the use of non-Gaussian operations on the CV resource channel can lead to a DV-qubit fidelity approaching unity for any channel loss.

Macroscopic Mechanical Entanglement Stability in Two Distant Dissipative Optomechanical Systems

AbstractA theoretical scheme for the stable entanglement generation of two remote mechanical modes is introduced. Two identical optomechanical systems, each constituting a single‐mode optical field as well as a qubit and a moveable mirror driven by an external pump field, are considered. To make the model more realistic, atomic, photonic, and phononic dissipations are considered. The time‐dependent state of each subsystem is obtained, analytically. Then, by an appropriate Bell‐state measurement (BSM) on the state of the whole system (first approach), the entanglement of two mechanical modes is created. As a second parallel approach, appropriate atomic measurement is applied after the BSM. According to these numerical simulations via concurrence, the noteworthy features are as follows. There exists optimum value of photon–phonon coupling strength for obtaining the steady‐state entanglement; by choosing appropriate values of dissipation, photon–phonon coupling, and pump amplitude, a significant degree and stable entanglement between the two mechanical modes are accessible. The present scheme opens new practical perspectives in constructing stable entanglement between two remote mechanical modes and can be helpful to realize quantum memories for quantum information processing and establishing long‐distance quantum communication networks.

Complete Bell state measurement of diamond nuclear spins under a complete spatial symmetry at zero magnetic field

The symmetry of the space where a spin qubit resides plays an essential role in the manipulation of quantum entanglement, which governs the performance of quantum information systems. Application of a magnetic field, which is usually necessary for spin manipulation and readout, inevitably breaks the spatial symmetry to induce competition among quantization axes between internal and external fields, thus limiting the purity of the entanglement. If we could manipulate and readout entanglement under a zero magnetic field, we would be able to avoid the competition among quantization axes to achieve ideally high fidelity. We here demonstrate the complete Bell state measurement, which is a core element of quantum processing, of two carbon nuclear spins in the vicinity of a diamond nitrogen-vacancy center. The demonstration was made possible by holonomic entanglement manipulations based on the geometric phase with a polarized microwave under a zero magnetic field, where the quantization axis is uniquely defined by the hyperfine field. The demonstrated scheme allows high-fidelity entanglement processing even when magnetic fields cannot be applied to the integration of superconducting and spin qubits, thereby paving the way for building fault-tolerant distributed quantum computers and quantum repeater networks.

Experimental demonstration of continuous-variable measurement-device-independent quantum key distribution over optical fiber

Measurement-device-independent quantum key distribution (MDI-QKD) can remove all side-channel attacks on detectors. In the context of the dramatic progress of discrete-variable MDI-QKD and twin-field QKD, owing to the critical challenge of continuous-variable (CV) Bell-state measurement (BSM) of two remote independent quantum states, experimental demonstration of CV-MDI-QKD over optical fiber has remained elusive. To solve this problem, a technology for CV-BSM of remote independent quantum states is developed that consists of optical phase locking, phase estimation, real-time phase feedback, and quadrature remapping in the present work. With this technology, CV-BSM is accurately implemented, and the first CV-MDI-QKD over optical fiber is demonstrated, to our knowledge. The achieved secret key rates are 0.43 (0.19) bits per pulse over a 5-km (10-km) optical fiber. Our work shows that it is feasible to build a CV-MDI-QKD system over optical fiber. Further, the results pave the way towards realization of a high secret key rate and low-cost metropolitan MDI-QKD network, and serve as a stepping stone to a CV quantum repeater.

Quantum State Transfer over 1200km Assisted by Prior Distributed Entanglement.

Long-distance quantum state transfer (QST), which can be achieved with the help of quantum teleportation, is a core element of important quantum protocols. A typical situation for QST based on teleportation is one in which two remote communication partners (Alice and Bob) are far from the entanglement source (Charlie). Because of the atmospheric turbulence, it is challenging to implement the Bell-state measurement after photons propagate in atmospheric channels. In previous long-distance free-space experiments, Alice and Charlie always perform local Bell-state measurement before the entanglement distribution process is completed. Here, by developing a highly stable interferometer to project the photon into a hybrid path-polarization dimension and utilizing the satellite-borne entangled photon source, we demonstrate proof-of-principle QST at the distance of over 1200km assisted by prior quantum entanglement shared between two distant ground stations with the satellite Micius. The average fidelity of transferred six distinct quantum states is 0.82±0.01, exceeding the classical limit of 2/3 on a single copy of a qubit.

Breaking the Rate-Loss Bound of Quantum Key Distribution with Asynchronous Two-Photon Interference

Twin-field quantum key distribution can overcome the secret key capacity of repeaterless quantum key distribution via single-photon interference. However, to compensate for the channel fluctuations and lock the laser fluctuations, the techniques of phase tracking and phase locking are indispensable in experiment, which drastically increase experimental complexity and hinder free-space realization. Inspired by the duality in entanglement, we herein present an asynchronous measurement-device-independent quantum key distribution protocol that can surpass the secret key capacity even without phase tracking and phase locking. Leveraging the concept of time multiplexing, asynchronous two-photon Bell-state measurement is realized by postmatching two interference detection events. For a 1 GHz system, the new protocol reaches a transmission distance of 450 km without phase tracking. After further removing phase locking, our protocol is still capable of breaking the capacity at 270 km. Intriguingly, when using the same experimental techniques, our protocol has a higher key rate than the phase-matching-type twin-field protocol. In the presence of imperfect intensity modulation, it also has a significant advantage in terms of the transmission distance over the sending-or-not-sending type twin-field protocol. With high key rates and accessible technology, our work provides a promising candidate for practical scalable quantum communication networks.

Probabilistic quantum teleportation of shared quantum secret

Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.

Bell state analyzer for spectrally distinct photons

We demonstrate a Bell state analyzer that operates directly on frequency mismatch. Based on electro-optic modulators and Fourier-transform pulse shapers, our quantum frequency processor design implements interleaved Hadamard gates in discrete frequency modes. Experimental tests on entangled-photon inputs reveal fidelities of ∼ 98 % for discriminating between the | Ψ + ⟩ and | Ψ − ⟩ frequency-bin Bell states. Our approach resolves the tension between wavelength-multiplexed state transport and high-fidelity Bell state measurements, which typically require spectral indistinguishability.

Measurement-Device-Independent Quantum Key Distribution of Frequency-Nondegenerate Photons

In measurement-device-independent quantum key distribution (MDI QKD), the setup of Bell state measurement (BSM) usually requires that the photons sent by different users should be frequency degenerate. It increases the complexity to implement MDI QKD since a complicated feedback system is usually required to calibrate photons' frequencies in different users. It also limits the development of MDI QKD networks since wavelength division multiplexing (WDM) technology is not compatible with this requirement. In this work, we propose a MDI QKD scheme of frequency-nondegenerate photons, in which the users send photons with different frequencies. It is based on a BSM setup with a frequency-domain beam splitter (FBS), which is realized by a phase modulator (PM). A proof-of-principle experiment is realized, showing that the BSM of frequency-nondegenerate photons could select specific users to realize MDI QKD by adjusting the modulation frequency of the PM to match the frequency difference of photons sent by the users. The results manifest that our scheme has great potential for simplifying the implementation and realizing MDI QKD networks combined with WDM.

Generation and dynamic manipulation of frequency degenerate polarization entangled Bell states by a silicon quantum photonic circuit

A silicon quantum photonic circuit was proposed and realized for the generation and the dynamic manipulation of telecom-band frequency-degenerate polarization entangled Bell states. Frequency degenerate biphoton states were generated in four silicon waveguides by spontaneous four wave mixing. They were transformed to polarization entangled Bell states through on-chip quantum interference and quantum superposition, and then coupled to optical fibers. The property of polarization entanglement in generated photon pairs was demonstrated by two-photon interference under two non-orthogonal polarization bases. The output state could be dynamically switched between two Bell states, which was demonstrated by the simplified Bell state measurement. The experiment results indicated that the manipulation speed supported a modulation rate of several tens kHz, showing its potential on applications of quantum communication and quantum information processing requiring Bell state encoding and dynamic control.

All-Optical Entanglement Swapping.

Entanglement swapping, which is a core component of quantum network and an important platform for testing the foundation of quantum mechanics, can enable the entangling of two independent particles without direct interaction both in discrete variable and continuous variable systems. Conventionally, the realization of entanglement swapping relies on the Bell-state measurement. In particular, for entanglement swapping in continuous variable regime, such Bell-state measurement involves the optic-electro and electro-optic conversion, which limits the applications of the entanglement swapping for constructing broadband quantum network. In this Letter, we propose and demonstrate a measurement-free all-optical entanglement swapping. In our scheme, a high-gain parametric amplifier based on the four-wave mixing process is exploited to realize the function of Bell-state measurement without detection, which avoids the introduction of the optic-electro and electro-optic conversion. Our results provide an all-optical paradigm for implementing entanglement swapping and pave the way to construct a measurement-free all-optical broadband quantum network.

Multi-hop entanglement swapping in quantum networks based on polization-space hyperentanglement

Entanglement swapping (ES) based multi-hop quantum information transmission is a fundamental way to realize long-distance quantum communication. However, in the conventional quantum networks, the entanglement in one degree of freedom (DOF) of photon system is usually used as a quantum channel, showing disadvantages of low capacity and susceptibility to noise. In this paper, we present an efficient multi-hop quantum hyperentanglement swapping (HES) method based on hyperentanglement, which utilizes the entangled photos in polarization and spatial-mode DOFs to establish the hyperentangled multi-hop quantum channel. Taking long-distance hyperentanglement based quantum teleportation for example, we first describe a basic hop by hop HES scheme. Then, in order to reduce the end-to-end delay of this scheme, we propose a simultaneous HES (SHES) scheme, in which the intermediate quantum nodes perform hyperentangled Bell state measurements concurrently. On the basis of this scheme, we further put forward a hierarchical SHES (HSHES) scheme that can reduce the classical information cost. Theoretical analysis and simulation results show that the end-to-end delay of HSHES is similar to that of SHES, meanwhile, the classical information cost of HSHES is much lower than that of SHES, showing a better tradeoff between the two performance metrics. Compared with the traditional ES methods, the scheme proposed in this paper is conductive to meeting the requirements for long-distance hyperentanglement based quantum communication, which has positive significance for building more efficient quantum networks in the future.

Measurement-device-independent quantum key distribution with classical Bob and no joint measurement

Measurement-device-independent quantum key distribution (MDI-QKD) provides a method for secret communication whose security does not rely on trusted measurement devices. In all existing MDI-QKD protocols, the participant Charlie has to perform the Bell state measurement or other joint measurements. Here we propose an MDI-QKD protocol which requires individual measurements only. Meanwhile, all operations of the receiver Bob are classical, without the need for preparing and measuring quantum systems. Thus the implementation of the protocol has a lower technical requirement on Bob and Charlie.

Loss-tolerant concatenated Bell-state measurement with encoded coherent-state qubits for long-range quantum communication

The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly-deterministic nature of the Bell-state measurement (BSM). However, its non-orthogonality incurs difficulties such as failure of the BSM. One may use a large amplitude ($\alpha$) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes ($|\alpha| \lessapprox 2$), which simultaneously suppresses both failures and dephasing in the BSM procedure. We numerically show that the CBSM scheme achieves a success probability arbitrarily close to unity for appropriate values of $\alpha$ and sufficiently low photon loss rates (e.g., $\lessapprox 5\%$). Furthermore, we verify that the quantum repeater scheme exploiting the CBSM scheme for quantum error correction enables one to carry out efficient long-range quantum communication over 1000 km. We show that the performance is comparable to those of other up-to-date methods or even outperforms them for some cases. Finally, we present methods to prepare logical qubits under modified parity encoding and implement elementary logical operations, which consist of several physical-level ingredients such as generation of Schr\"odinger's cat state and elementary gates under coherent-state basis. Our work demonstrates that the encoded coherent-state qubits in free-propagating fields provide an alternative route to fault-tolerant information processing, especially long-range quantum communication.

Experimental realization of quantum controlled teleportation of arbitrary two-qubit state via a five-qubit entangled state

Quantum controlled teleportation is the transmission of the quantum state under the supervision of a third party. This paper presents the theoretical and experimental results of an arbitrary two-qubit quantum controlled teleportation scheme, in which the sender Alice only needs to perform two Bell state measurements and the receiver Bob can perform an appropriate unitary operation to reconstruct the arbitrary two-qubit states under the control of the supervisor Charlie. The operation process of the scheme is verified on the IBM quantum experience platform, and the accuracy of the transmitted quantum state is further checked by performing quantum state tomography. Meanwhile, a good fidelity is obtained by using the theoretical density matrix and the experimental density matrix. A sequence of photonic states is introduced to analyze the possible intercept–replace–resend, intercept–measure–resend, and entanglement–measure–resend attacks on this scheme. The results proved that our scheme is highly secure.

Hybrid Entanglement between Optical Discrete Polarizations and Continuous Quadrature Variables

By coherently combining advantages while largely avoiding limitations of two mainstream platforms, optical hybrid entanglement involving both discrete and continuous variables has recently garnered widespread attention and emerged as a promising idea for building heterogenous quantum networks. In contrast to previous results, here we propose a new scheme to remotely generate hybrid entanglement between discrete polarization and continuous quadrature optical qubits heralded by two-photon Bell-state measurement. As a novel nonclassical light resource, we further use it to discuss two examples of ways—entanglement swapping and quantum teleportation—in which quantum information processing and communications could make use of this hybrid technique.

Error-correcting entanglement swapping using a practical logical photon encoding

Several emerging quantum technologies, including quantum networks, modular and fusion-based quantum computing, rely crucially on the ability to perform photonic Bell state measurements. Therefore, photon losses and the 50\% success probablity upper bound of Bell state measurements pose a critical limitation to photonic quantum technologies. Here, we develop protocols that overcome these two key challenges through logical encoding of photonic qubits. Our approach uses a tree graph state logical encoding, which can be produced deterministically with a few quantum emitters, and achieves near-deterministic logical photonic Bell state measurements while also protecting against errors including photon losses, with a record loss-tolerance threshold.