High-fidelity four-photon GHZ states on chip

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 $${{{{\mathcal{F}}}}}_{{{{{\rm{GHZ}}}}}_{4}}=(86.0\pm 0.4)\, \%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>GHZ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mn>86.0</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mspace/> <mml:mi>%</mml:mi> </mml:mrow> </mml:math> , and a purity of $${{{{\mathcal{P}}}}}_{{{{{\rm{GHZ}}}}}_{4}}=(76.3\pm 0.6)\, \%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>GHZ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mn>76.3</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.6</mml:mn> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mspace/> <mml:mi>%</mml:mi> </mml:mrow> </mml:math> . 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.