Hyperentanglement, which refers to entanglement encoded in two or more independent degrees of freedom (DOFs), is a valuable resource for the future high-capacity quantum network. Certifying hyperentanglement sources work as intended is critical for the hyperentanglement-based quantum information tasks. Self testing is the strongest certification method for quantum state and measurement under minimal assumptions, even without any knowledge of the devices' inner workings. However, the existing self testing protocols all focus on one-DOF entanglement, which cannot self test the multi-DOF entanglement. In the paper, we propose a hyperentanglement self testing framework. We take the self testing for the polarization-spatial-mode hyperentangled Bell states as an example. The self testing is based on the violation of two-dimension CHSH test in each DOF independently. The two-step swap isometry circuits are proposed for self testing the entanglement in spatial-mode and polarization DOFs, respectively. All the sixteen polarization-spatial-mode hyperentangled Bell states can be self tested. Our hyperentanglement self testing framework has three advantages. First, it is a general hyperentanglement self testing framework, and can be extended to self test multi-DOF hyperentanglement and multipartite hyperentanglement. Second, it can provide the robust hyperentanglement self testing and establish the relation between the lower bound of fidelity and the imperfect violation of Bell-like inequality in each DOF. Third, it is feasible with current experimental technology. Our hyperentanglement self testing framework provides a promising way to certify complex hyperentanglement sources, and has potential application in future high-capacity quantum network.
Hyperentanglement, which refers to entanglement encoded in two or more independent degrees of freedom (DOFs), is a valuable resource for the future high-capacity quantum network. Certifying hyperentanglement sources work as intended is critical for the hyperentanglement-based quantum information tasks. Self testing is the strongest certification method for quantum state and measurement under minimal assumptions, even without any knowledge of the devices' inner workings. However, the existing self testing protocols all focus on one-DOF entanglement, which cannot self test the multi-DOF entanglement. In the paper, we propose a hyperentanglement self testing framework. We take the self testing for the polarization-spatial-mode hyperentangled Bell states as an example. The self testing is based on the violation of two-dimension CHSH test in each DOF independently. The two-step swap isometry circuits are proposed for self testing the entanglement in spatial-mode and polarization DOFs, respectively. All the sixteen polarization-spatial-mode hyperentangled Bell states can be self tested. Our hyperentanglement self testing framework has three advantages. First, it is a general hyperentanglement self testing framework, and can be extended to self test multi-DOF hyperentanglement and multipartite hyperentanglement. Second, it can provide the robust hyperentanglement self testing and establish the relation between the lower bound of fidelity and the imperfect violation of Bell-like inequality in each DOF. Third, it is feasible with current experimental technology. Our hyperentanglement self testing framework provides a promising way to certify complex hyperentanglement sources, and has potential application in future high-capacity quantum network.
Abstract Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell’s theorem, one can infer the appearance of certain entangled state when the maximum violation is observed, e.g., to self-test singlet state using CHSH inequality. In this work, by constructing a versatile entanglement source, we experimentally demonstrate a generalized self-testing proposal for various bipartite entangled states up to four dimensions. We show that the high-quality generated states can approach the maximum violations of the utilized Bell inequalities, and thus, their Schmidt coefficients can be precisely inferred by self-testing them into respective target states with near-unity fidelities. Our results indicate the superior completeness and robustness of this method and promote self-testing as a practical tool for developing quantum techniques.
Bell state measurements, of which the eigenvectors are in an entangled form, are crucial resources in the construction of quantum networks. Therefore, device-independent certification of a Bell state measurement has significance in the quantum information process because it satisfies the exact demand on security. In this study, we implement a proof-of-concept experiment to certify a Bell state measurement device independently in an entanglement swapping process, namely, self-testing. Instead of preparing a tensor product of two singlets with four photons, multiplex encoding in polarization and spatial modes is utilized to produce two pairs of entangled qubits. As a result, we implement a full Bell state measurement and achieve a high degree of Bell violation on the remaining two qubits, which are required for nontrivial self-testing of a Bell state measurement. Furthermore, our results combine the correlations before and after the swapping; thus, the quality of the performed Bell state measurement can be precisely inferred.
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.
Robust self-testing of the m−partite maximally entangled state and observables
As quantum technologies continue to advance rapidly, the device-independent testing of the functioning of a quantum device has become increasingly important. Self-testing, a correlation based protocol, enables such certification of a promised quantum state as well as measurements performed on it without requiring knowledge of the device's internal workings. This approach typically relies on achieving the optimal quantum violation of a suitable Bell inequality. Self-testing has been extensively investigated in the context of bipartite Bell experiments. However, its extension to multipartite scenarios remains largely unexplored, owing to the intricate nature of multipartite quantum correlations. In this work, we propose a simple and efficient self-testing protocol that certifies the state and observables based on the optimal quantum violation of the Svetlichny inequality involving an arbitrary number of parties, each with two inputs. Our method leverages an elegant sum-of-squares approach to derive the optimal quantum value of the Svetlichny functional, devoid of assuming the dimension of the quantum system. This enables the self-testing of the m−partite maximally entangled state and local anti-commuting observables for each party. Moreover, we develop a swap circuit isometry to assess the proximity of reference states and measurements to their ideal counterparts in the presence of noise and imperfections in real experiments, thereby demonstrating the robustness of our self-testing protocol. Finally, we illustrate how our self-testing protocol facilitates the generation of certified genuine randomness from correlations that enable the optimal violation of the Svetlichny inequality.
According to the properties of the hyperentangled Bell state and hyper-encoding technology, this paper proposes a high-capacity quantum key distribution protocol with qudits hyper-encoded in polarization and spatial mode degrees of freedom (DOFs). In our protocol, 8 bits of information can be transmitted in one iteration. In contrast, the previous quantum key distribution protocols can only transmit up to 4 or 6 bits in one iteration. Moreover, quantum memory is unnecessary in our protocol. We analyze the relationship between the amount of eavesdropping and the success rate of eavesdropping. With the increase of eavesdropping information, the eavesdropping success probability will decrease sharply. The results show that our protocol is secure. Finally, this protocol is flexible; each qubit has two completely independent DOFs. If one DOF is destroyed, the other can still be used to transmit secure information. The protocol may be useful in the future quantum communication field.
Abstract We present two deterministic hyperentangled state analysis protocols for photons entangled in polarization, spatial-mode and time-bin degrees of freedom (DOFs). The first protocol is a hyperentangled Bell state analyzer, and the second is a hyperentangled Greenberger–Horne–Zeilinger (GHZ) state analyzer for three photons. In the first scheme, we construct a polarization parity-check quantum nondemolition detector (P-QND) and a spatial-mode parity-check quantum nondemolition detector (S-QND) based on cross-Kerr nonlinearities. With these P-QND and S-QND, we design the setup of Bell state analyzer in polarization and spatial-mode DOFs. While time-bin entanglement is discriminated with the help of the polarization entanglement. We generalize the idea to analyze the three-photon hyperentangled GHZ states. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely discriminated via three steps. These two state analysis schemes are expected to provide practical applications for high-capacity and long-distance quantum communication.