Loophole-free Bell inequality violation with superconducting circuits

Abstract

Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality1–3 can be experimentally demonstrated in Bell tests4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes5 succeeded. Such experiments have been performed with spins in nitrogen–vacancy centres6, optical photons7–9 and neutral atoms10. Here we demonstrate a loophole-free violation of Bell’s inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology11. To evaluate a Clauser–Horne–Shimony–Holt-type Bell inequality4, we deterministically entangle a pair of qubits12 and perform fast and high-fidelity measurements13 along randomly chosen bases on the qubits connected through a cryogenic link14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell’s inequality with a P value smaller than 10−108. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics15.

Improving quantum state transfer: correcting non-Markovian and distortion effects

“…To compensate for the distortions that appear in a medium with non-linear dispersion relations, we derived a new set of control equations that both address the need of complex couplings, while introducing corrections beyond the usual Markovian theory. Both ingredients combine to reduce the infidelity of quantum state transfer for several orders of magnitude in scenarios of practical experimental interest, such as circuit-QED experiments involving long quantum links as those employed in [37,38]. For short quantum links, i.e.…”

“…It is worth mentioning that no decoherence effects have been included as we aim at improving the fidelity of the fully-coherent quantum state transfer. For reference, however, photon losses can spoil the fidelity by 0.5% or less for a L = 60 m waveguide according to [37,38]. As we will see below, this loss can be comparable or even a smaller effect than the infidelity resulting from photon distortion alone.…”

“…In this work we address both limitations simultaneously without compromising the speed of state transfer, which is of particular relevance for long quantum links, such as in the recent experiments in [37,38]. We consider a fully-coherent transfer and solve the photon dispersion problem by imprinting the flying qubit with engineered phases and frequency chirps that compensate for the errors in the quantum link.…”

Quantum Nonlocality: How Does Nature Do It?

“…According to LRHVM, a probability that some cyclic combinations of pairwise expectations violate Bell–CHSH inequalities is tending to 0, if sample sizes are increasing to infinity. Since a significant violation of the inequalities was reported in several loophole-free Bell tests [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ], one might conclude that neither LRHVM nor stochastic hidden variable model (SHVM) [ 18 ] provided a correct description of these experiments.…”

“…Section 9 contains our conclusions. In the Appendix A , we present in some detail experimental protocols used in the most recent Bell tests [ 10 , 15 , 16 , 17 ].…”