Bell's inequality violation with spins in silicon

Abstract

Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states. For this reason the Bell signal has been tagged as a single-number benchmark for the performance of quantum computing devices. Here we demonstrate deterministic, on-demand generation of two-qubit entangled states of the electron and the nuclear spin of a single phosphorus atom embedded in a silicon nanoelectronic device. By sequentially reading the electron and the nucleus, we show that these entangled states violate the Bell/CHSH inequality with a Bell signal of 2.50(10). An even higher value of 2.70(9) is obtained by mapping the parity of the two-qubit state onto the nuclear spin, which allows for high-fidelity quantum non-demolition measurement (QND) of the parity. Furthermore, we complement the Bell inequality entanglement witness with full two-qubit state tomography exploiting QND measurement, which reveals that our prepared states match the target maximally entangled Bell states with $>$96\% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom, and show that this system is able to maintain its simultaneously high initialization, manipulation and measurement fidelities past the single-qubit regime.

10 pages, 3 figures, 1 table, 4 extended data figures

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• Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits
• Loopholes in Bell Inequality Tests of Local Realism
• Demonstration of entanglement-by-measurement of solid state qubits
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Cited by in corpus (45)

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• Certified randomness in quantum physics
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• Local and Distributed Quantum Computation
• Quantum-Coherent Nanoscience
• Performing Quantum Computing Experiments in the Cloud
• Tailoring spin defects in diamond
• Coherent spin qubit transport in silicon
• Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis
• Donor spins in silicon for quantum technologies
• A silicon quantum-dot-coupled nuclear spin qubit
• Spatial Metrology of Dopants in Silicon with Exact Lattice Site Precision
• Breaking the rotating wave approximation for a strongly-driven, dressed, single electron spin
• Delayed entanglement echo for individual control of a large number of nuclear spins
• Long-distance entangling gates between quantum dot spins mediated by a superconducting resonator
• Grover's algorithm in a four-qubit silicon processor above the fault-tolerant threshold
• Exploring quantum chaos with a single nuclear spin
• Chained Bell Inequality Experiment with High-Efficiency Measurements
• Characterization of the Si:Se+ spin-photon interface
• Bell correlations between light and vibration at ambient conditions
• Coherent control via weak measurements in ${}^{31}$P single-atom electron and nuclear spin qubits
• Roadmap on Atomic-scale Semiconductor Devices
• Beating the thermal limit of qubit initialization with a Bayesian Maxwell's demon
• Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits
• Detecting many-body Bell non-locality by solving Ising models
• Controllable Single Cooper Pair Splitting in Hybrid Quantum Dot Systems
• Electro-optomechanical equivalent circuits for quantum transduction
• On the Feasibility of Bell Inequality Violation at ATLAS Experiment with Flavor Entanglement of $B^0{\bar{B}}^0$ Pairs from $pp$ Collisions
• Entanglement and quantum state geometry of spin system with all-range Ising-type interaction
• Violating Bell's inequality in gate-defined quantum dots
• Approaching ideal visibility in singlet-triplet qubit operations using energy-selective tunneling-based Hamiltonian estimation
• Scalable entanglement of nuclear spins mediated by electron exchange
• Zero field optical magnetic resonance study of phosphorus donors in 28-silicon
• Probing two-qubit capacitive interactions beyond bilinear regime using dual Hamiltonian parameter estimations
• Higher-Dimensional Bell Inequalities with Noisy Qudits
• Hyperfine-assisted decoherence of a phosphorus nuclear-spin qubit in silicon
• A Computational Workflow for Designing Silicon Donor Qubits
• Quantum contextuality of complementary photon polarizations explored by adaptive input state control
• Indistinguishability between quantum randomness and pseudo-randomness under efficiently calculable randomness measures
• Predictive tracking of the NV Center based on external temperature sensors
• Four-state discrimination for a pair of spin qubits via gate reflectometry
• Quantum correlations and coherence in a two-qubit anisotropic $XY$ under magnetic field
• Electron readout contrast enhancement in the parallel nuclear regime of an exchange-coupled donor spin qubit system