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npj Quantum Information

High-fidelity four-photon GHZ states on chip

Mathias Pont, Giacomo Corrielli, Andreas Fyrillas, Iris Agresti, Gonzalo Carvacho, Nicolas Maring, Pierre-Emmanuel Emeriau, Francesco Ceccarelli, Riccardo Albiero, Paulo Henrique Dias Ferreira, Niccolò Somaschi, Jean Sénellart, Isabelle Sagnes, Martina Morassi, Aristide Lemaître, P. Senellart, Fabio Sciarrino, Marco Liscidini, Nadia Belabas, Roberto Osellame

Published May 15, 2024• 44 citations
Publisher

Abstract

Abstract Mutually entangled multi-photon states are at the heart of all-optical quantum technologies. While impressive progresses have been reported in the generation of such quantum light states using free space apparatus, high-fidelity high-rate on-chip entanglement generation is crucial for future scalability. In this work, we use a bright quantum-dot based single-photon source to demonstrate the high fidelity generation of 4-photon Greenberg-Horne-Zeilinger (GHZ) states with a low-loss reconfigurable glass photonic circuit. We reconstruct the density matrix of the generated states using full quantum-state tomography reaching an experimental fidelity to the target state of $${{{{\mathcal{F}}}}}_{{{{{\rm{GHZ}}}}}_{4}}=(86.0\pm 0.4)\, \%$$ F GHZ 4 = ( 86.0 ± 0.4 ) % , and a purity of $${{{{\mathcal{P}}}}}_{{{{{\rm{GHZ}}}}}_{4}}=(76.3\pm 0.6)\, \%$$ P GHZ 4 = ( 76.3 ± 0.6 ) % . The entanglement of the generated states is certified with a semi device-independent approach through the violation of a Bell-like inequality by more than 39 standard deviations. Finally, we carry out a four-partite quantum secret sharing protocol on-chip where a regulator shares with three interlocutors a sifted key with up to 1978 bits, achieving a qubit-error rate of 10.87%. These results establish that the quantum-dot technology combined with glass photonic circuitry offers a viable path for entanglement generation and distribution.

DOI
10.1038/s41534-024-00830-z

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Abstract Mutually entangled multi-photon states are at the heart of all-optical quantum technologies. While impressive progresses have been reported in the generation of such quantum light states using free space apparatus, high-fidelity high-rate on-chip entanglement generation is crucial for future scalability. In this work, we use a bright quantum-dot based single-photon source to demonstrate the high fidelity generation of 4-photon Greenberg-Horne-Zeilinger (GHZ) states with a low-loss reconfigurable glass photonic circuit. We reconstruct the density matrix of the generated states using full quantum-state tomography reaching an experimental fidelity to the target state of FGHZ4=(86.0±0.4) %{{{{\mathcal{F}}}}}_{{{{{\rm{GHZ}}}}}_{4}}=(86.0\pm 0.4)\, \%FGHZ4​​=(86.0±0.4)% F GHZ 4 = ( 86.0 ± 0.4 ) % , and a purity of PGHZ4=(76.3±0.6) %{{{{\mathcal{P}}}}}_{{{{{\rm{GHZ}}}}}_{4}}=(76.3\pm 0.6)\, \%PGHZ4​​=(76.3±0.6)% P GHZ 4 = ( 76.3 ± 0.6 ) % . The entanglement of the generated states is certified with a semi device-independent approach through the violation of a Bell-like inequality by more than 39 standard deviations. Finally, we carry out a four-partite quantum secret sharing protocol on-chip where a regulator shares with three interlocutors a sifted key with up to 1978 bits, achieving a qubit-error rate of 10.87%. These results establish that the quantum-dot technology combined with glass photonic circuitry offers a viable path for entanglement generation and distribution.
Mutually entangled multi-photon states are at the heart of all-optical quantum technologies. While impressive progresses have been reported in the generation of such quantum light states using free space apparatus, high-fidelity high-rate on-chip entanglement generation is crucial for future scalability. In this work, we use a bright quantum-dot based single-photon source to demonstrate the high fidelity generation of 4-photon Greenberg-Horne-Zeilinger (GHZ) states with a low-loss reconfigurable glass photonic circuit. We reconstruct the density matrix of the generated states using full quantum-state tomography reaching an experimental fidelity to the target ∣GHZ4⟩|{\text{GHZ}_4}\rangle∣GHZ4​⟩ of FGHZ4(86.0±0.4) %\mathcal{F}_{\text{GHZ}_4} (86.0\pm0.4)\,\%FGHZ4​​(86.0±0.4)%, and a purity of PGHZ4=(76.3±0.6) %\mathcal{P}_{\text{GHZ}_4}=(76.3\pm0.6)\,\%PGHZ4​​=(76.3±0.6)%. The entanglement of the generated states is certified with a semi device-independent approach through the violation of a Bell-like inequality by more than 39 standard deviations. Finally, we carry out a four-partite quantum secret sharing protocol on-chip where a regulator shares with three interlocutors a sifted key with up to 1978 bits, achieving a qubit-error rate of 10.87 %10.87\,\%10.87%. These results establish that the quantum-dot technology combined with glass photonic circuitry for entanglement generation on chip offers a viable path for intermediate scale quantum computation and communication.
We present a programmable silicon photonic four-qubit integrated circuit for the generation and manipulation of diverse quantum states. The silicon photonic chip integrates photon-pair sources, pump-reducing filters, wavelength-division-multiplexing filters, Mach–Zehnder interferometer switches, and single-qubit arbitrary gates, enabling versatile state preparation and tomography. We measure Hong–Ou–Mandel interference with an impressive 98% visibility using four-photon coincidence, laying the foundation for high-purity qubits. Our analysis involves estimating the fidelity and purity of distinct quantum states through maximum-likelihood estimation applied to tomographic measurements. In our experimental results, we showcase the following achievements: a heralded single qubit achieving 98.2% fidelity and 98.3% purity, a Bell state reaching 95.2% fidelity and 94.8% purity, and a four-qubit system with two simultaneous Bell states exhibiting 87.4% fidelity and 84.6% purity. Finally, a four-qubit Greenberger–Horne–Zeilinger (GHZ) state demonstrates 85.4% fidelity and 81.7% purity. In addition, we certify the entanglement of the four-photon GHZ state through Bell’s inequality violations and a negative entanglement witness.
We present an experiment where a reconfigurable photonic processor fabricated in glass by femtosecond laser micromachining is used for the generation of four-photons GHZ entangled states, with high efficiency and fidelity. The chip is used in synergy with a bright and quasi-deterministic source of single photons based on semiconductor quantum dot. The very efficient interfacing of these two platforms is ensured by the excellent connectivity between glass photonic circuits and standard optical fibers. In addition, in order to benchmark the quality of the generated states, this processor is used to implement a quantum secret sharing protocol on chip.
Abstract Encoding high-dimensional quantum information into single photons can provide a variety of benefits for quantum technologies, such as improved noise resilience. However, the efficient generation of on-demand, high-dimensional entanglement was thought to be out of reach for current and near-future photonic quantum technologies. We present a protocol for the near-deterministic generation of N-photon, d-dimensional photonic Greenberger–Horne–Zeilinger (GHZ) states using an array of d non-interacting single-photon emitters. We analyse the impact on performance of common sources of error for quantum emitters, such as photon spectral distinguishability and temporal mismatch, and find they are readily correctable with time-resolved detection to yield high fidelity GHZ states of multiple qudits. When applied to a quantum key distribution scenario, our protocol exhibits improved loss tolerance and key rates when increasing the dimensionality beyond binary encodings.
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)≤F≤0.881(17)0.841(17) \leq \mathcal{F} \leq 0.881(17)0.841(17)≤F≤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.