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Laser Physics Letters

Complete hyperentangled Bell state analysis assisted by hyperentanglement

Zhi Zeng, Ka-Di Zhu

Published Jun 24, 2020• 12 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ab9117

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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.
Hyperentanglement represents a key resource in many quantum information processing schemes. Here, we present a complete and fidelity-robust hyperentangled-Bell-state analysis (HBSA) scheme for two-photon systems entangled in polarization, spatial mode, and time-bin degrees of freedom (DOFs). The scheme uses a fidelity-robust quantum nondemolition (QND) detector called BLOCK1, built with a singly charged semiconductor quantum dot (QD) in a double-sided optical microcavity (double-sided QD-cavity system) under the balance condition, and some linear-optical elements. Compared with the previously proposed complete HBSA schemes based on ideal optical giant circular birefringence, our scheme guarantees the robust fidelity and relaxes the requirement on the QD-cavity parameters with the assistance of the balance condition. Different from the schemes using error-detected blocks and exchanging Bell states in different DOFs to get unity fidelity, the BLOCK1 under the balance condition can directly measure the Bell states of polarization and spatial mode so that fewer kinds of linear optical components are needed in our scheme. In addition, our scheme simplifies the discrimination process and reduces the required light–matter interaction by using a self-assisted mechanism. These features indicate that our scheme may be directly generalized to multiphoton hyperentangled Greenberger–Horne–Zeilinger state analysis and more feasible in practical quantum applications based on the photonic hyperentanglement.
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 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.
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.
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.
Abstract Hyperentangled states can outperform their classical counterparts on solving certain tasks. Here, a simplified scheme for completely distinguishing two‐photon hyperentangled Bell states in polarization, spatial, and time‐bin degrees of freedom (DOFs) is presented. Unity fidelity can be achieved in principle without strong couple limitation between photon and quantum dot (QD), and the incomplete and imperfect QD‐cavity interactions are prevented by single‐photon detectors. In addition, auxiliary photons or DOFs are not required in the scheme. The necessary linear optical elements are fewer than the parity‐check‐based one.