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Optics Express

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

Cong Cao, Li Zhang, Yu‐Hong Han, Pan-Pan Yin, Ling Fan, Yuwen Duan, Ru Zhang

Published Jan 11, 2020• 50 citations
Publisher

Abstract

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.

DOI
10.1364/oe.384360

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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.
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 construct an error-detected block, assisted by the quantum-dot spins in double-sided optical microcavities. With this block, we propose three error-detected schemes for the deterministic generation, the complete analysis, and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom of two-photon systems. In these schemes, the errors can be detected, which can improve their fidelities largely, far different from other previous schemes assisted by the interaction between the photon and the QD-cavity system. Our scheme for the deterministic generation of hyperentangled two-photon systems can be performed by repeat until success. These features make our schemes more useful in high-capacity quantum communication with hyperentanglement in the future.
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 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.
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.
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.