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arXiv:2304.05683 · Quantum Science and Technology

Generation of a time–bin Greenberger–Horne–Zeilinger state with an optical switch

Hsin-Pin Lo, Takuya Ikuta, Koji Azuma, Toshimori Honjo, William J. Munro, Hiroki Takesue

Published Mar 27, 2023• 14 citations

Abstract

Abstract Multipartite entanglement is a critical resource in quantum information processing that exhibits much richer phenomenon and stronger correlations than in bipartite systems. This advantage is also reflected in its multi-user applications. Although many demonstrations have used photonic polarization qubits, polarization-mode dispersion confines the transmission of photonic polarization qubits through an optical fiber. Consequently, time–bin qubits have a particularly important role to play in quantum communication systems. Here, we generate a three-photon time–bin Greenberger–Horne–Zeilinger (GHZ) state using a 2 × 2 optical switch as a time-dependent beam splitter to entangle time–bin Bell states from a spontaneous parametric down-conversion source and a weak coherent pulse. To characterize the three-photon time–bin GHZ state, we performed measurement estimation, showed a violation of the Mermin inequality, and used quantum state tomography to fully reconstruct a density matrix, which shows a state fidelity exceeding 70%. We expect that our three-photon time–bin GHZ state can be used for long-distance multi-user quantum communication.

DOI: 10.1088/2058-9565/acc7c2

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Abstract Multipartite entanglement is a critical resource in quantum information processing that exhibits much richer phenomenon and stronger correlations than in bipartite systems. This advantage is also reflected in its multi-user applications. Although many demonstrations have used photonic polarization qubits, polarization-mode dispersion confines the transmission of photonic polarization qubits through an optical fiber. Consequently, time–bin qubits have a particularly important role to play in quantum communication systems. Here, we generate a three-photon time–bin Greenberger–Horne–Zeilinger (GHZ) state using a 2 × 2 optical switch as a time-dependent beam splitter to entangle time–bin Bell states from a spontaneous parametric down-conversion source and a weak coherent pulse. To characterize the three-photon time–bin GHZ state, we performed measurement estimation, showed a violation of the Mermin inequality, and used quantum state tomography to fully reconstruct a density matrix, which shows a state fidelity exceeding 70%. We expect that our three-photon time–bin GHZ state can be used for long-distance multi-user quantum communication.

We study Greenberger-Horne-Zeilinger--type (GHZ-type) and

W

-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for

W

-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate

W

-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the

W

-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

We experimentally demonstrate a high-fidelity entanglement swapping and a generation of the Greenberger-Horne-Zeilinger (GHZ) state using polarization-entangled photon pairs at telecommunication wavelength produced by spontaneous parametric down conversion with continuous-wave pump light. While spatially separated sources asynchronously emit photon pairs, the time-resolved photon detection guarantees the temporal indistinguishability of photons without active timing synchronizations of pump lasers and/or adjustment of optical paths. In the experiment, photons are sufficiently narrowed by fiber-based Bragg gratings with the central wavelengths of 1541 nm & 1580 nm, and detected by superconducting nanowire single-photon detectors with low timing jitters. The observed fidelities of the final states for entanglement swapping and the generated three-qubit state were 0.84 ± 0.04 and 0.70 ± 0.05, respectively.

Distributed entanglement across multi-node quantum networks is essential for a wide range of quantum technologies, including modular quantum computers, distributed sensing and metrology, and multi-party secure communication protocols. Such large-scale quantum networks will require photonic interconnects to generate and sustain entangled states across localized nodes. Previously, three-node distributed Greenberger-Horne-Zeilinger (GHZ) states have been generated between solid-state qubits and atomic ensembles, but not yet in the platform of individual atomic qubits, which can be replicated, detected, and individually controlled with high fidelity. Here we report the first fully-distributed GHZ state of qubits across a three-node quantum network of single atomic memories, using photonic interconnects. We achieve a bounded fidelity of

0.841(17) \leq \mathcal{F} \leq 0.881(17)

at an entanglement generation rate of 0.095(5)/sec and measure a clear violation of Mermin's inequality while closing the detection loophole for the first time in a fully-distributed multipartite entangled state.

The next generation of telecommunication networks will rely on the transmission of complex quantum states to enable secure and transformative information processing, utilizing entanglement and superposition. Cluster states - multipartite entangled states that retain entanglement under local measurements - are a vital resource for quantum networking applications such as blind photonic quantum computing, quantum state teleportation and all-photonic quantum repeaters. However, the transmission of cluster states over optical fiber has remained elusive with previous approaches. Here, we demonstrate the first transmission of a four-qubit cluster state over 25 km of single-mode fiber by using a two-photon multi-level time-bin encoding. We directly generate the state by exploiting coherent control of a parametric generation process, rendering a resource-intensive controlled-phase gate obsolete. To enable efficient and reconfigurable projective measurements on the multi-level time-bin encoded state, we introduce chirped-pulse modulation and implement the first time-bin beam splitter, allowing us to certify genuine multipartite entanglement and to demonstrate one-way computing operations. Our approach enables the transmission of complex quantum states over long-distance fibers, permitting the implementation of multipartite protocols and laying the foundation for large-scale quantum resource networks.