Bell-state Measurement Research Articles

Multi-party quantum private comparison of size relationship with two third parties based on d-dimensional Bell states

In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting -dimensional Bell states, which can judge the size relationship of private integers from more than two users within one execution of protocol. Each TP is permitted to misbehave on her own but cannot collude with others. In the proposed MQPC protocol, TPs are only required to apply -dimensional single-particle measurements rather than -dimensional Bell state measurements. There are no quantum entanglement swapping and unitary operations required in the proposed MQPC protocol. The security analysis validates that the proposed MQPC protocol can resist both the outside attacks and the participant attacks. The proposed MQPC protocol is adaptive for the case that users want to compare the size relationship of their private integers under the control of two supervisors. Furthermore, the proposed MQPC protocol can be used in the strange user environment, because there are not any communication and pre-shared key between each pair of users.

Teleportation of unknown states of a qubit and a single-mode field in strong coupling regime without Bell-state measurement

In this paper, we develop the teleportation scheme in [Zheng in Phys Rev A 69, 064302, 2004], in the sense that, we work in the strong atom-field coupling regime wherein the rotating wave approximation (RWA) is no longer valid. To achieve the purpose, a scheme consisting of a qubit interacting with a single-mode quantized field is described via the Rabi model (counter rotation terms are taken into account). Our first aim is to teleport an unknown atomic state of a qubit (which interacts with the quantized field in a cavity) to a second qubit (exists in another distant cavity field), beyond the RWA and without the Bell-state measurement method. In the continuation, in a similar way, we teleport an unknown state of a single-mode field too. In fact, it is shown that, in this regime, after applying some particular conditions, containing the interaction time of atom-field in the cavities, adjusting the involved frequencies, as well as the atom-field coupling in the model, if a proper measurement is performed on the state of the first qubit (the related field in the cavity), the unknown states of the qubit (field) can be teleported from the first qubit (cavity field) to the second qubit (cavity field), appropriately. We show that in both considered cases, the teleportation protocol is successfully performed with the maximum possible fidelity, 1, and the acceptable success probability, 0.25.

Detector entanglement: Quasidistributions for Bell-state measurements

Measurements in the quantum domain can exceed classical notions. This concerns fundamental questions about the nature of the measurement process itself, as well as applications, such as their function as building blocks of quantum information processing protocols. In this paper we explore the notion of entanglement for detection devices in theory and experiment. A method is devised that allows one to determine nonlocal quantum coherence of positive-operator-valued measures via negative contributions in a joint distribution that fully describes the measurement apparatus under study. This approach is then applied to experimental data for detectors that ideally project onto Bell states. In particular, we describe the reconstruction of the aforementioned entanglement quasidistributions from raw data and compare the resulting negativities with those expected from theory. Therefore, our method provides a versatile toolbox for analyzing measurements regarding their quantum-correlation features for quantum science and quantum technology.

Probabilistic Quantum Teleportation via 3-Qubit Non-maximally Entangled GHZ State by Repeated Generalized Measurements

We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $\sigma_{x}$. Both these measurement outcomes are communicated to Bob classically, which helps him to perform a suitable unitary transformation on qubit 3 to recover the information state. On the other hand, if failure is obtained, the next attempt of GBSM is performed on qubits 0 and 2. This process of repeating GBSM on alternate pair of qubits may continue until perfect teleportation with unit fidelity is achieved. We have obtained analytical expressions for success probability up to three repetitions of GBSM. The success probability is shown to be a polynomial function of bipartite concurrence of the NME resource. The variation of success probability with the bipartite concurrence has been plotted which shows the convergence of success probability to unity with GBSM repetitions.

Measurement-device-independent quantum protocol for Private Set Intersection/ Union Cardinality

In this paper, we present a novel measurement-device-independent quantum protocol for Private Set Intersection/ Union Cardinality. This protocol takes weak coherent pulses in the BB84 polarization states as quantum resources, instead of ideal single photons, and only needs to perform Bell state identifications, instead of perfect Bell state measurements. With the current technology, our protocol has better feasibility and higher security than the related quantum protocol. Finally, we verify the correctness and feasibility of the proposed quantum protocol by circuit simulations in IBM Qiskit.

Metasurface for complete measurement of polarization Bell state

AbstractBell state measurement is vital to quantum information technology. Conventional linear optical elements, however, cannot fully distinguish all polarization Bell states without assisting of additional degrees of freedom. Leveraging on a pair of binary-pixel metasurfaces, we demonstrate direct measurement of all four polarization Bell states. Each metasurface is designed to produce two output modes that linearly superpose three Bell states in the coincidence counting measurement. By rotating the polarizers, the coincidence counting measurement achieves a tunable anticorrelation between one and the other two Bell states, achieving Bell state detection efficiency of 75% in a single measurement. Complete and deterministic Bell state measurement is further realized by performing two measurements. Our work shows the advantage of utilization of metasurfaces in quantum detection schemes and is of great applicative interest for quantum dense coding, entanglement swapping, quantum teleportation protocols, and novel quantum information processing tasks.

General scheme for complete high-dimensional Bell state measurement.

We theoretically propose a simple and efficient scheme for the complete analysis of high-dimensional Bell states in N dimensions. The mutually orthogonal high-dimensional entangled states can be unambiguously distinguished by obtaining the parity and relative phase information of entanglement independently. Based on this approach, we present the physical realization of photonic four-dimensional Bell state measurement with the current technology. The proposed scheme will be useful for quantum information processing tasks that utilize high-dimensional entanglement.

Two-Photon Interference of Single Photons from Dissimilar Sources

Entanglement swapping and heralding are at the heart of many protocols for distributed quantum information. For photons, this typically involves Bell-state measurements based on two-photon interference effects. In this context, hybrid systems that combine high rate, ultrastable, and pure quantum sources with long-lived quantum memories are particularly interesting. Here, we develop a theoretical description of pulsed two-photon interference of photons from dissimilar sources to predict the outcomes of second-order cross-correlation measurements. These are directly related to, and hence used to quantify, photon indistinguishability. We study their dependence on critical system parameters such as quantum state lifetime and emission frequency, and quantify the impact of time jitter, pure dephasing, and spectral wandering. We show that for a fixed lifetime of one of the two emitters, for each frequency detuning there is an optimal lifetime of the second emitter that leads to the highest photon indistinguishability. Expectations for different hybrid combinations involving III-V semiconductor quantum dots, color centers in diamond, atom-scale defects in two-dimensional materials and neutral atoms are quantitatively compared for real-world system parameters. Our work provides a theoretical basis for the treatment of dissimilar emitters and enables assessment of which imperfections can be tolerated in hybrid photonic quantum networks.

Security research on practical measurement-device-independent quantum key distribution

The ideal measurement-device-independent quantum key distribution (MDI-QKD), which is immune to all detector side-channel attacks, is built on the Bell state measurement of two single-photon states. However, in practical MDI-QKD where phase-randomized weak coherent pulses (PR-WCPs) are used, the mismatch between states preparation and measurement in X basis leads to the bit error rate of more than 25%, which poses a challenge to the security of QKD. In this paper, we provide a security analysis of practical MDI-QKD based on polarization coding. We analyze the Hong-Ou-Mandel interference of PR-WCPs and Poisson-distributed photon number states (PNs), and find that these two sources are equivalent in MDI-QKD. The security analysis based on entanglement distillation is carried out on PNs, and the measurement results in Z basis and X basis are averaged to overcome the noncorrelation of the error rates in these two bases. Compared with GLLP scheme, a tighter key rate is obtained in this work, and the key rate deviates from the linear key rate bound in a short distance due to the finite proportion of multiphoton terms.

Semi-quantum key distribution with two classical users

Semi-quantum key distribution (SQKD) is an important research issue which allows one quantum participant equipped with advanced quantum devices to distribute a shared secret key securely with one classical user who has restricted capabilities. In this paper, we propose a SQKD protocol which allows one quantum user to distribute two different private secret keys to two classical users respectively at the same time. Alice distributes two particle sequences from Bell states to Bob and Charlie respectively. Once the particles have been processed and returned, Alice can simultaneously detect reflected particles by Bob and Charlie based on Bell-state measurement and generate two different raw keys. To enable more participants in sharing keys, this protocol can be extended to the m + 1 party communication scheme by employing m-particle GHZ state. In large-scale communication networks, this extended model significantly reduces the complexity of communication compared to the traditional SQKD scheme. Security analyses show that the presented protocol is free from several general attacks, such as the entangle-measure attack, the modification attack, the double CNOT attack, and so on.

Teleportation of hybrid entangled states with continuous-variable entanglement

Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified protocol in teleporting CV-only qubits, showing that significant improvement over traditional CV-based teleportation is obtained. We then explore similar modifications in the teleportation of a specific hybrid entangled state showing that significant improvement over traditional CV-based teleportation is again found. For a given channel loss, we find teleporting the DV qubit of the hybrid entangled state can always achieve higher fidelity than teleporting the CV qubit. We then explore the use of various non-Gaussian operations in our modified teleportation protocol, finding that, at a cost of lower success probability, quantum scissors provides the most improvement in the loss tolerance. Our new results emphasize that in lossy conditions, the quantum measurements undertaken at the sender can have a surprising and dramatic impact on CV-based teleportation.

Two Quantum Proxy Blind Signature Schemes Based on Controlled Quantum Teleportation

We present a scheme for teleporting an unknown, two-particle entangled state with a message from a sender (Alice) to a receiver (Bob) via a six-particle entangled channel. We also present another scheme for teleporting an unknown one-particle entangled state with a message transmitted in a two-way form between the same sender and receiver via a five-qubit cluster state. One-way hash functions, Bell-state measurements, and unitary operations are adopted in these two schemes. Our schemes use the physical characteristics of quantum mechanics to implement delegation, signature, and verification processes. Moreover, a quantum key distribution protocol and a one-time pad are adopted in these schemes.

Long distance measurement-device-independent three-party quantum key agreement

Key agreement is a basic cryptographic primitive, which plays an important role in private communications. In this work, we propose a measurement-device-independent three-party quantum key agreement protocol and then analyze its security, which shows that it can guarantee both the security and fairness for key agreement. Furthermore, this protocol is based on Greenberger–Horne–Zeilinger states while only Bell state measurements and single-particle state measurements are required, and therefore it is experimentally feasible with current technology. More importantly, this protocol can double the space distance between participants for quantum transmission by placing untrusted relays in the middle compared with conventional protocols.

Quantum asymmetric cyclic teleportation of arbitrary single-particle and two-particle states

In this paper, two three-party cyclic teleportation schemes for real arbitrary quantum states of a single particle and two particles are proposed for the first time. In the first ([Formula: see text]) scheme, Alice sends any single particle state to Bob, Bob sends any two-particle states to Charlie, and meanwhile Charlie sends any single particle state to Alice. In the second ([Formula: see text]) scheme, with the help of the controller David, Alice sends any two-particle states to Bob, Bob sends any two-particle states to Charlie, and Charlie sends any single particle state to Alice simultaneously. Based on the maximum entangled quantum channel shared in advance, the communication participants carry out some Bell state measurement (BSM) measurements and carry out corresponding unitary transformation according to the results published by each other. After that, the cyclic teleportation of predetermined quantum information can be successfully realized. The success probability of teleportation of both schemes can reach 100%. Finally, this paper briefly analyzes the security of the two schemes and compares them with some previously published schemes from the perspective of inherent efficiency. The results show that the two schemes proposed in this paper are safe and have high inherent efficiency. Different from the previous symmetric cyclic quantum teleportation methods, the asymmetric cyclic quantum teleportation schemes proposed in this paper are more universal.

Remote entanglement distribution in a quantum network via multinode indistinguishability of photons

Quantum networking relies on entanglement distribution between distant nodes, typically realized by swapping procedures. However, entanglement swapping is a demanding task in practice, mainly because of limited effectiveness of entangled photon sources and Bell-state measurements necessary to realize the process. Here we experimentally activate a remote distribution of two-photon polarization entanglement superseding the need for initial entangled pairs and traditional Bell-state measurements. This alternative procedure is accomplished thanks to the controlled spatial indistinguishability of four independent photons in three separated nodes of the network, which enables us to perform localized product-state measurements in the central node acting as a trigger. This experiment proves that the inherent indistinguishability of identical particles supplies new standards for feasible quantum communication in multinode photonic quantum networks.

Four-dimensional orbital angular momentum Bell-state measurement assisted by the auxiliary polarization and path degrees of freedom.

The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.

Measurement-device-independent one-step quantum secure direct communication

The one-step quantum secure direct communication (QSDC) (Sci. Bull. 67, 367 (2022)) can effectively simplify QSDC’s operation and reduce message loss. For enhancing its security under practical experimental condition, we propose two measurement-device-independent (MDI) one-step QSDC protocols, which can resist all possible attacks from imperfect measurement devices. In both protocols, the communication parties prepare identical polarization-spatial-mode two-photon hyperentangled states and construct the hyperentanglement channel by hyperentanglement swapping. The first MDI one-step QSDC protocol adopts the nonlinear-optical complete hyperentanglement Bell state measurement (HBSM) to construct the hyperentanglement channel, while the second protocol adopts the linear-optical partial HBSM. Then, the parties encode the photons in the polarization degree of freedom and send them to the third party for the hyperentanglement-assisted complete polarization Bell state measurement. Both protocols are unconditionally secure in theory. The simulation results show the MDI one-step QSDC protocol with complete HBSM attains the maximal communication distance of about 354 km. Our MDI one-step QSDC protocols may have potential applications in the future quantum secure communication field.

Detecting a Photon-Number Splitting Attack in Decoy-State Measurement-Device-Independent Quantum Key Distribution via Statistical Hypothesis Testing.

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols also need the decoy-state method, which can resist PNS attacks very well. However, the existing decoy-state methods do not attend to the existence of PNS attacks, and the secure keys are only generated by single-photon components. In fact, multiphoton pulses can also form secure keys if we can confirm that there is no PNS attack. For simplicity, we only analyze the weaker version of a PNS attack in which a legitimate user’s pulse count rate changes significantly after the attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state MDI-QKD protocols via statistical hypothesis testing, extract a normal distribution statistic, and provide a detection method and the corresponding Type I error probability. If the result is judged to be an attack, we use the existing decoy-state method to estimate the secure key rate. Otherwise, all pulses with the same basis leading to successful Bell state measurement (BSM) events including both single-photon pulses and multiphoton pulses can be used to generate secure keys, and we give the formula of the secure key rate in this case. Finally, based on actual experimental data from other literature, the associated experimental results (e.g., the significance level is 5%) show the correctness of our method.

Four-Qubit Cluster States Generation through Multi-Coin Quantum Walk

Quantum computing requires large numbers of resources of entangled qubits, which cannot be satisfied using traditional methods of entanglement generation, such as optical systems. Therefore, we need more efficient ways of entanglement generation. It has been proved that multi-coin quantum walks can be used to replace direct Bell state measurements during the process of entanglement generation in order to avoid the difficulty of Bell state measurement. In this paper, we take one step further and generate 4-qubit cluster states using multi-coin quantum walks, which simplifies the generation of 4-qubit cluster states by using only Bell states and local measurements. We also propose a method for preparing 4-qubit cluster states with quantum circuits to facilitate their use in quantum computing.

Deployed measurement-device independent quantum key distribution and Bell-state measurements coexisting with standard internet data and networking equipment

The forthcoming quantum Internet is poised to allow new applications not possible with the conventional Internet. The ability for both quantum and conventional networking equipment to coexist on the same fiber network would facilitate the deployment and adoption of coming quantum technology. Most quantum networking tasks, like quantum repeaters and the connection of quantum processors, require nodes for multi-qubit quantum measurements (often Bell-State measurements), and their real-world coexistence with the conventional Internet has yet to be shown. Here we field deploy a Measurement-Device Independent Quantum Key Distribution (MDI-QKD) system, containing a Bell-State measurement node, over the same fiber connection as multiple standard Internet Protocol (IP) data networks, between three nearby cities in the Netherlands. We demonstrate over 10 Gb/s classical data communication rates simultaneously with our next-generation QKD system, and estimate 200 GB/s of classical data transmission would be easily achievable without significantly affecting QKD performance. Moreover, as the system ran autonomously for two weeks, this shows an important step towards the coexistence and integration of quantum networking into the existing telecommunication infrastructure.