Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km

Abstract: For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Bell showed that in any local realist theory the correlations between distant measurements satisfy an inequality and, moreover, that this inequality can be violated according to quantum theory. This provided a recipe for experimental tests of the fundamental principles underlying the laws of nature. In the past decades, numerous ingenious Bell inequality tests have been reported. However, because of experimental limitations, all experiments to date required additional assumptions to obtain a contradiction with local realism, resulting in loopholes. Here we report on a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We employ an event-ready scheme that enables the generation of high-fidelity entanglement between distant electron spins. Efficient spin readout avoids the fair sampling assumption (detection loophole), while the use of fast random basis selection and readout combined with a spatial separation of 1.3 km ensure the required locality conditions. We perform 245 trials testing the CHSH-Bell inequality $S \leq 2$ and find $S = 2.42 \pm 0.20$. A null hypothesis test yields a probability of $p = 0.039$ that a local-realist model for space-like separated sites produces data with a violation at least as large as observed, even when allowing for memory in the devices. This result rules out large classes of local realist theories, and paves the way for implementing device-independent quantum-secure communication and randomness certification.

• The paper demonstrates a loophole-free Bell test using entangled NV electron spins separated by 1.3 km.
• It employed rigorous random measurements on independent NV center qubits and achieved a CHSH inequality violation with S = 2.42 ± 0.20.
• The results reinforce quantum nonlocality and support future device-independent quantum communication and secure network developments.

Loop-Free Bell Test with Entangled Electron Spins Over 1.3 km

The violation of Bell inequalities holds significant implications for the foundational understanding of quantum mechanics, specifically concerning the principle of local realism, which insists upon both locality and realism. This paper reports an experimental test that closes several longstanding loopholes associated with previous attempts to empirically validate Bell's theorem. The researchers conducted a Bell test that closes both the "locality loophole" and the "detection loophole" using entangled electron spins separated by a considerable distance of 1.3 km.

Theoretical Context

Bell's theorem posits that no physical theory of local hidden variables can reproduce all the predictions of quantum mechanics. A Bell inequality, derived from this theorem, provides a stringent test to differentiate between quantum predictions and those based on classical local realism. The theorem suggests that quantum correlations exceed the bounds predicted by classical theories, where the combination of locality (no faster-than-light influences) and realism (pre-determined physical properties) define the described correlation bounds.

Experimental Methodology

The experimental design implemented herein involves entangled electron spins embedded in nitrogen-vacancy (NV) centers situated within diamond structures, effectively serving as qubits. Each qubit is engineered and controlled independently, with random measurements introducing one of the inputs to the system. The researchers used a Clauser-Horne-Shimony-Holt (CHSH) inequality version which contrasts correlations in pairs of distant quantum systems.

The experiment involved three spatially separated locations (A, B, and C), where NV electron spins were independently manipulated and measured. The device at location C facilitated the detection of photons indicative of successful events, which is key to the event-ready architecture. Importantly, the spatial configuration ensured that the local events at A and B remained space-like separated, thus preserving the integrity of the locality condition.

Key Results

The experiment constitutes 245 independent trials testing the CHSH-Bell inequality $S \leq 2$, where they observed $S = 2.42 \pm 0.20$. This significant violation of Bell’s inequality strongly dismisses local realist models under two rigorous statistical analyses: a conventional one and a complete analysis encompassing potential memory effects within the devices and imperfections in random number generation.

A complete statistical analysis yielded a p-value of $0.039$ for rejecting the local realist hypothesis, assuming no trial independence or distribution-specific assumptions. These results bolster the empirical rejection of local realist interpretations of quantum mechanics and endorse entanglement as a fundamental quantum phenomenon.

Implications and Future Work

This research serves as a critical validation of quantum nonlocality, heralding device-independent applications such as quantum-secure communication and randomness certification, which rely on entanglement across great distances. By experimentally closing major loopholes in Bell tests, this work not only reaffirms quantum mechanics's predictions but also opens potential pathways for technological advancements in secure quantum networks.

Future endeavors may aim at expanding the experimental distances further, refining system fidelity, and enhancing entanglement production rates. Additionally, variations in input bit sources and positions could assert stricter constraints on freedom-of-choice assumptions, offering deeper insights into the philosophical implications of quantum theory foundations. Future implementations, potentially involving quantum repeaters and advanced photonic structures, may facilitate large-scale, loophole-free quantum networks, grounded in principles substantiated by the very tests employed in this study.