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New Journal of Physics

Complete hyperentangled state analysis using weak cross-Kerr nonlinearity and auxiliary entanglement

Zhi Zeng, Ka-Di Zhu

Published Jul 10, 2020• 13 citations
Publisher

Abstract

Abstract We present a new method for the complete analysis of hyperentangled Bell state and Greenberger–Horne–Zeilinger state in polarization and spatial-mode degrees of freedom, resorting to weak cross-Kerr nonlinearity and auxiliary frequency entanglement. The weak cross-Kerr nonlinearity with small phase shift is used to construct quantum nondestructive detector, and it is realizable with the current technology. Compared with the previous schemes, our scheme largely reduces the requirement on nonlinearity with the help of auxiliary entanglement in the third degree of freedom. Our method provides an efficient avenue for the hyperentangled state analysis, and will be useful for high-capacity quantum information processing.

DOI
10.1088/1367-2630/aba465

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Abstract We present a new method for the complete analysis of hyperentangled Bell state and Greenberger–Horne–Zeilinger state in polarization and spatial-mode degrees of freedom, resorting to weak cross-Kerr nonlinearity and auxiliary frequency entanglement. The weak cross-Kerr nonlinearity with small phase shift is used to construct quantum nondestructive detector, and it is realizable with the current technology. Compared with the previous schemes, our scheme largely reduces the requirement on nonlinearity with the help of auxiliary entanglement in the third degree of freedom. Our method provides an efficient avenue for the hyperentangled state analysis, and will be useful for high-capacity quantum information processing.
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.
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 NNN-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.
Hyperentanglement, the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention as it can be used to increase both the channel capacity of quantum communication and its security largely. Here, we present the first scheme to completely distinguish the hyperentangled Bell states of two-photon systems in three DOFs with the help of cross-Kerr nonlinearity without destruction, including two longitudinal momentum DOFs and the polarization DOF. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors which can be used to make a parity-check measurement and analyze Bell states of two-photon systems in different DOFs. Our complete scheme for two-photon six-qubit hyperentangled Bell-state analysis may be useful for the practical applications in quantum information, especially in long-distance high-capacity quantum communication.
Abstract 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.
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.
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.