Hyperentangled Bell State Analysis Research Articles

Complete analysis of hyperentangled Bell state in three degrees of freedom using Kerr effect and self-assisted mechanism

We present an efficient scheme for the complete hyperentangled Bell state analysis (HBSA) of photon system with polarization and two longitudinal momentum degrees of freedom (DOFs), resorting to weak cross-Kerr nonlinearity, linear optical elements and single photon detectors. In the process of distinguishing the 64 hyperentangled Bell states in three DOFs, the self-assisted mechanism is embedded, which makes our scheme simple and realizable. Moreover, we have discussed the applications of this complete HBSA scheme for high-capacity quantum communication protocols that are based on photonic hyperentanglement in three DOFs.

Self-assisted deterministic hyperentangled-Bell-state analysis for polarization and double longitudinal momentum degrees of freedom of photon system

Hyperentangled state analysis is an important module in high-capacity quantum communication. We present a self-assisted deterministic hyperentangled-Bell-state analysis (HBSA) scheme for photon system entangled in three degrees of freedom (DOFs), where 64 polarization-double longitudinal momentum hyperentangled Bell states are completely distinguished. In this HBSA scheme, the four first longitudinal momentum Bell states are distinguished determinately by nondestructive first longitudinal momentum Bell state analyzer, which is constructed with cross-Kerr nonlinearity medium. The 16 second longitudinal momentum-polarization hyperentangled Bell states are distinguished determinately by self-assisted second longitudinal momentum-polarization hyperentangled Bell state analyzer using linear optical elements, where the first longitudinal momentum Bell state and time-bin entangled state are used as auxiliary. Using this self-assisted method, the application of nonlinear optical resource in HBSA scheme has been largely reduced, which makes this self-assisted deterministic HBSA scheme has potential application prospects in high-capacity quantum communication.

Complete analysis of the maximally hyperentangled state via the weak cross-Kerr nonlinearity

We present a simple method for the complete analysis of the maximally hyperentangled state in polarization and spatial-mode degrees of freedom assisted by the weak cross-Kerr nonlinearity. Our method can not only be used for two-photon hyperentangled Bell state analysis and three-photon hyperentangled Greenberger–Horne–Zeilinger (GHZ) state analysis, but is also suitable for N -photon hyperentangled GHZ state analysis. In our protocols, the bit information of hyperentanglement is read out via the nonlinear interaction, and the phase information is obtained by using linear optical element and single photon detector. This approach is achievable with the current technology, and it will be useful for practical high-capacity quantum communication schemes.

Feasible high-dimensional measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD) can resist all possible attacks from practical measurement devices. High-dimensional (HD) MDI-QKD in multiple degrees of freedom (DOFs) can efficiently increase the key generation rate and has strong noise and error resistance. However, previous HD MDI-QKD protocols in multiple DOFs required complete hyperentangled Bell state analysis (HBSA), which cannot be realized under current experimental conditions and largely limits the practicality of the HD MDI-QKD. In this paper, we propose an HD MDI-QKD protocol in multiple DOFs which adopts a linear-optical HBSA. This adoption of the linear-optical HBSA makes our HD MDI-QKD feasible under current experimental technology. The key generation rate of our MDI-QKD protocol is about eight times of the original MDI-QKD protocol. Our HD MDI-QKD protocol may have potential applications in current and future quantum communication fields.

Deterministic nondestructive state analysis for polarization-spatial-time-bin hyperentanglement with cross-Kerr nonlinearity* *Project supported by the National Natural Science Foundation of China (Grant No. 11604226) and Science and Technology Program Foundation of the Beijing Municipal Commission of Education of China (Grants No. CIT&TCD201904080).

We present a deterministic nondestructive hyperentangled Bell state analysis protocol for photons entangled in three degrees of freedom (DOFs), including polarization, spatial-mode, and time-bin DOFs. The polarization Bell state analyzer and spatial-mode Bell state analyzer are constructed by polarization parity-check quantum nondemolition detector (P-QND) and spatial-mode parity-check quantum nondemolition detector (S-QND) using cross-Kerr nonlinearity, respectively. The time-bin Bell state analyzer is constructed by the swap gate for polarization state and time-bin state of a photon (P-T swap gate) and P-QND. The Bell states analyzer for one DOF will not destruct the Bell states of other two DOFs, so the polarization-spatial-time-bin hyperentangled Bell states can be determinately distinguished without destruction. This deterministic nondestructive state analysis method has useful applications in quantum information protocols.

Complete hyperentangled Bell state analysis assisted by hyperentanglement

We present a simple scheme for the complete analysis of hyperentangled Bell states in polarization and spatial-mode degrees of freedom (DOFs) assisted by time-bin–frequency hyperentanglement. In previous schemes of distinguishing the 16 hyperentangled Bell states, many non-linear interaction systems are widely used to construct a quantum gate, such as cross-Kerr non-linearity, quantum-dot spin in an optical microcavity and nitrogen-vacancy centers in a resonator. In our scheme, we utilize the time-bin and frequency DOFs of a photon system as the auxiliary DOFs to analyze polarization–spatial-mode hyperentangled Bell states, and the distinguishing principle is quite different from the former schemes that use the non-linear interactions. As the manipulation of time-bin and frequency DOFs of photons is efficient and feasible with current technology, this scheme will be useful for high-capacity quantum information processing based on hyperentanglement.

Complete and faithful hyperentangled-Bell-state analysis of photon systems using a failure-heralded and fidelity-robust quantum gate.

Hyperentangled-Bell-state analysis (HBSA) represents a key step in many quantum information processing schemes that utilize hyperentangled states. In this paper, we present a complete and faithful HBSA scheme for two-photon quantum systems hyperentangled in both the polarization and spatial-mode degrees of freedom, using a failure-heralded and fidelity-robust quantum swap gate for the polarization states of two photons (P-SWAP gate), constructed with a singly charged semiconductor quantum dot (QD) in a double-sided optical microcavity (double-sided QD-cavity system) and some linear-optical elements. Compared with the previously proposed complete HBSA schemes using different auxiliary tools such as parity-check quantum nondemonlition detectors or additional entangled states, our scheme significantly simplifies the analysis process and saves the quantum resource. Unlike the previous schemes based on the ideal optical giant circular birefringence induced by a single-electron spin in a double-sided QD-cavity system, our scheme guarantees the robust fidelity and relaxes the requirement on the QD-cavity parameters. These features indicate that our scheme may be more feasible and useful in practical applications based on the photonic hyperentanglement.

Error-heralded generation and self-assisted complete analysis of two-photon hyperentangled Bell states through single-sided quantum-dot-cavity systems

Hyperentangled Bell-state analysis (HBSA) is critical for high-capacity quantum communication. Here we design two effective schemes for error-heralded deterministic generation and self-assisted complete analysis of hyperentangled Bell states for two-photon systems in both the polarization and spatial-mode degrees of freedom, assisted by single-sided quantum-dot-cavity systems. We construct an error-heralded block with a singly charged quantum dot inside a single-sided optical microcavity, two circular polarization beam splitters, one half-wave plate, and one single-photon detector, in which the errors due to imperfect interactions between photons and quantum dot systems can be heralded. With this error-heralded block, the fidelity of our two schemes for hyperentangled Bell-state generation and complete HBSA can reach unit one. What interesting is that by using the measured spatial-mode state to assist the analysis of the polarization state, our complete HBSA scheme works in a self-assisted way, which greatly simplifies the analysis process and largely relaxes the requirements on nonlinearities. These advantages make our schemes much easier to implement experimentally, and have more practical applications in long-distance high-capacity quantum communication.

Self-assisted complete hyperentangled Bell state analysis using quantum-dot spins in optical microcavities

An efficient scheme for the discrimination of 16 hyperentangled Bell states of a two-photon system that is entangled in both polarization and spatial-mode degrees of freedom is presented in this paper. Using the interaction between the photons and quantum-dot spins in cavities, the spatial-mode Bell states can be distinguished completely and nondestructively in the first step. Subsequently, the preserved spatial-mode entanglement is utilized as an auxiliary to analyze the polarization Bell states. Compared with a previous scheme (Ren et al 2012 Opt. Express 20 24664–77), our scheme reduces the requirement for nonlinear interaction substantially by utilizing the intrinsic degrees of freedom in hyperentanglement.

Complete hyperentangled Bell state analysis for polarization and time-bin hyperentanglement.

We present a complete hyperentangled Bell state analysis protocol for two-photon four-qubit states that are simultaneously entangled in the polarization and time-bin degrees of freedom. The 16 hyperentangled states can be unambiguously distinguished via two steps. In the first step, the polarization entangled state is distinguished deterministically and nondestructively with the help of the cross-Kerr nonlinearity. Then, in the second step, the time-bin state is analyzed with the aid of the polarization entanglement. We also discuss the applications of our protocol for quantum information processing. Compared with hyperentanglement in polarization and spatial-mode degrees of freedom, the polarization and time-bin hyperentangled states provide savings in quantum resources since there is no requirement for two spatial modes for each photon. This is the first complete hyperentangled Bell state analysis scheme for polarization and time-bin hyperentangled states, and it can provide new avenues for high-capacity, long-distance quantum communication.

Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity

We present two complete maximally hyperentangled state analysis protocols for photons entangled in the polarization and spatial-mode degrees of freedom. The first protocol is a hyperentangled Bell state analysis scheme for two photons and the second is a hyperentangled Greenberger-Horne- Zeilinger (GHZ) state analysis scheme for three photons. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely and deterministically discriminated with the aid of cross-Kerr nonlinearities and linear optics. We also generalize the schemes to unambiguously analyze the N-photon hyperentangled GHZ state. Compared with previous protocols, our schemes greatly simplify the discrimination process and reduce the requirements on nonlinearities by using the measured spatial-mode state to assist in the analysis of the polarization state. These advantages make our schemes useful for practical applications in long-distance high capacity quantum communication.

Complete hyperentangled-Bell-state analysis for photonic qubits assisted by a three-level Λ-type system.

Hyperentangled Bell-state analysis (HBSA) is an essential method in high-capacity quantum communication and quantum information processing. Here by replacing the two-qubit controlled-phase gate with the two-qubit SWAP gate, we propose a scheme to distinguish the 16 hyperentangled Bell states completely in both the polarization and the spatial-mode degrees of freedom (DOFs) of two-photon systems. The proposed scheme reduces the use of two-qubit interaction which is fragile and cumbersome, and only one auxiliary particle is required. Meanwhile, it reduces the requirement for initializing the auxiliary particle which works as a temporary quantum memory, and does not have to be actively controlled or measured. Moreover, the state of the auxiliary particle remains unchanged after the HBSA operation, and within the coherence time, the auxiliary particle can be repeatedly used in the next HBSA operation. Therefore, the engineering complexity of our HBSA operation is greatly simplified. Finally, we discuss the feasibility of our scheme with current technologies.

Complete Distributed Hyper-Entangled-Bell-State Analysis and Quantum Super Dense Coding

We propose a protocol to implement the distributed hyper-entangled-Bell-state analysis (HBSA) for photonic qubits with weak cross-Kerr nonlinearities, QND photon-number-resolving detection, and some linear optical elements. The distinct feature of our scheme is that the BSA for two different degrees of freedom can be implemented deterministically and nondestructively. Based on the present HBSA, we achieve quantum super dense coding with double information capacity, which makes our scheme more significant for long-distance quantum communication.

Hyper-parallel photonic quantum computation and manipulation on hyperentangled states

Photon system is a promising candidate for quantum information processing, and it can be used to achieve some important tasks with the interaction between a photon and an atom (or a artificial atom), such as the transmission of secret information, the storage of quantum states, and parallel quantum computing. Several degrees of freedom (DOFs) of a photon system can be used to carry information in the realization of quantum information processing, such as the polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs. A hyperparallel quantum computer can implement the quantum operations on several DOFs of a quantum system simultaneously, which reduces the operation time and the resources consumed in quantum information processing. The hyperparallel quantum operations are more robust against the photonic dissipation noise than the quantum computing in one DOF of a photon system. Hyperentanglement, defined as the entanglement in several DOFs of a quantum system, can improve the channel capacity and the security of long-distance quantum communication, and it can also be conductive to completing some important tasks in quantum communication. Hyperentangled Bell-state analysis is used to completely distinguish the 16 hyperentangled Bell states, which is very useful in high-capacity quantum communication protocols and quantum repeaters. In order to depress the effect of noises in quantum channel, hyperentanglement concentration and hyperentanglement purification are required to improve the entanglement of the quantum systems in long-distance quantum communication, which is also very useful in high-capacity quantum repeaters. Hyperentanglement concentration is used to distill several nonlocal photon systems in a maximally hyperentangled state from those in a partially hyperentangled pure state, and hyperentanglement purification is used to distill several nonlocal photon systems in a high-fidelity hyperentangled state from those in a mixed hyperentangled state with less entanglement. In this reviewing article, we review some new applications of photon systems with multiple DOFs in quantum information processing, including hyperparallel photonic quantum computation, hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification.