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arXiv:1511.00094 · Scientific Reports

Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity

Qian Liu, Guan-Yu Wang, Qing Ai, Mei Zhang, Fu‐Guo Deng

Published Feb 25, 2016• 54 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/srep22016

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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.
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.
We present an efficient hyperentanglement concentration protocol (hyper-ECP) for two-photon six-qubit systems in nonlocal partially hyperentangled Bell states with unknown parameters. In our scheme, we use two identical partially hyperentangled states which are simultaneously entangled in polarization and two different longitudinal momentum degrees of freedom (DOFs) to distill the maximally hyperentangled Bell state. The quantum nondemolition detectors based on the cross-Kerr nonlinearity are used to realize the parity checks of two-photon systems in three DOFs. The hyper-ECP can extract all the useful entanglement source, and the success probability can reach the theory limit with the help of iteration. All these advantages make our hyper-ECP useful in long-distance quantum communication in the future.
We present two hyperentangled concentration schemes for two-photon systems in a partially hyperentangled Bell state that is simultaneously entangled in polarization, spatial mode and time-bin degrees of freedom (DOFs). The first scheme extracts a maximally hyperentangled Bell state using cross-Kerr nonlinearity, which is discussed in two cases of unknown and known coefficients. We construct quantum nondemolition detectors based on cross-Kerr nonlinearities to implement the polarization and spatial parity check. In this scheme, we only require a small phase shift, as long as it can be distinguished from zero. The second scheme is used to concentrate an initial partially hyperentangled state with only linear optical elements, where coefficients of the initial state are known. Both of the two schemes are feasible with the current experimental technology. Moreover, hyperentanglement DOFs can largely improve the channel capacity of long-distance quantum communication. All of these make our schemes more practical and useful in quantum communication.
Abstract 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.
Hyperentanglement is the quantum system entangled in several degrees of freedom (DOFs), which has attracted extensive attention in quantum communication. In the practical application of hyperentanglement, the key step is to know the information of the hyperentanglement. In this paper, we propose an efficient protocol to measure the concurrence of arbitrary two-photon six-qubit hyperentangled state, which simultaneously entangles in the polarization and double longitudinal momentum DOFs. This protocol requires the weak cross-Kerr nonlinearity and some linear optical elements to construct the quantum nondemolition detection gate. The concurrence in each DOF can be converted into the success probability of distilling some specified states. Our protocol may play an important role in future quantum information processing.
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.