Bell inequality violation in gate-defined quantum dots

Paul Steinacker (), Tuomo Tanttu, Wee Han Lim, Nard Dumoulin Stuyck, MengKe Feng, Santiago Serrano, Ensar Vahapoglu, Rocky Y. Su, Jonathan Y. Huang, Cameron Jones, Kohei M. Itoh, Fay E. Hudson, Christopher C. Escott, Andrea Morello, Andre Saraiva, Chih Hwan Yang, Andrew S. Dzurak () and Arne Laucht ()
Additional contact information
Paul Steinacker: University of New South Wales
Tuomo Tanttu: University of New South Wales
Wee Han Lim: University of New South Wales
Nard Dumoulin Stuyck: University of New South Wales
MengKe Feng: University of New South Wales
Santiago Serrano: University of New South Wales
Ensar Vahapoglu: University of New South Wales
Rocky Y. Su: University of New South Wales
Jonathan Y. Huang: University of New South Wales
Cameron Jones: University of New South Wales
Kohei M. Itoh: Keio University
Fay E. Hudson: University of New South Wales
Christopher C. Escott: University of New South Wales
Andrea Morello: University of New South Wales
Andre Saraiva: University of New South Wales
Chih Hwan Yang: University of New South Wales
Andrew S. Dzurak: University of New South Wales
Arne Laucht: University of New South Wales

Nature Communications, 2025, vol. 16, issue 1, 1-9

Abstract: Abstract Quantum computers leverage entanglement to achieve superior computational power. However, verifying that the entangled state does not follow the principle of local causality has proven difficult for spin qubits in gate-defined quantum dots, as it requires simultaneously high concurrence values and readout fidelities to break the classical bound imposed by Bell’s inequality. While low error rates for state preparation, control, and measurement have been independently demonstrated, a simultaneous demonstration remained challenging. We employ advanced protocols like heralded initialization and calibration via gate set tomography (GST), to push fidelities of the full 2-qubit gate set above 99%, including state preparation and measurement (SPAM). We demonstrate a 97.17% Bell state fidelity without correcting for readout errors and violate Bell’s inequality using direct parity readout with a Bell signal of S = 2.731. Our measurements exceed the classical limit even at 1.1 K or entanglement lifetimes of 100 μs. Violating Bell’s inequality in a silicon quantum dot qubit system is a key milestone, as it proves quantum entanglement, fundamental to achieving quantum advantage.

Date: 2025
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DOI: 10.1038/s41467-025-57987-0

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