Loophole-Free Bell Tests

A Bell violation refutes local hidden variables only if the experiment actually meets the theorem's assumptions. For decades, every test left a loophole — a way a clever local model could fake the data. Closing all of them simultaneously was achieved in 2015. This lesson catalogues the loopholes and how they were shut.

The locality loophole

Bell's argument assumes the two measurements are space-like separated: neither setting choice nor outcome can influence the other within the round, even at light speed. If the apparatuses are too close or too slow, a sub-light-speed signal could in principle coordinate the outcomes.

Closing it requires that the entire event on Alice's side — choosing a random setting, performing the measurement, and recording the outcome — finish before any light-speed signal from Bob's setting choice could arrive, and vice versa. This demands fast random-setting generation and a large separation; the 2015 NV-centre experiment used $1.3\ \mathrm{km}$ , giving a $\sim 4.3\ \mu\mathrm{s}$ light-crossing budget that comfortably exceeded the measurement duration.

The detection (fair-sampling) loophole

If detectors miss many particles, the detected subensemble may violate a Bell inequality even when the full ensemble is perfectly local — the lost events could be conspiratorially biased. Avoiding the fair-sampling assumption requires the detection efficiency $\eta$ to exceed a threshold; for the CHSH inequality with maximal entanglement the threshold is $\eta > 2(\sqrt2 - 1) \approx 0.828$ , relaxable toward $2/3$ with non-maximally-entangled states (the Eberhard bound).

The freedom-of-choice loophole

Bell assumes the settings are chosen independently of the hidden variable $\lambda$ (measurement independence). If some common cause influenced both $\lambda$ and the setting choices, a local model could survive. Experiments address this with fast quantum or pseudo-random number generators placed so that the choice is space-like separated from the source emission; the "BIG Bell Test" even crowd- sourced setting bits from human volunteers, and "cosmic Bell tests" used light from distant quasars to push the common-cause origin billions of years into the past.

The 2015 loophole-free experiments

The decisive demonstration (Hensen et al., 2015) entangled the electron spins of two nitrogen-vacancy centres in diamonds $1.3\ \mathrm{km}$ apart via entanglement swapping through emitted photons, heralded so that only successful entangling events were kept — which sidesteps the detection loophole because the spin readout, not the heralding photon, carries near-unit efficiency. Random fast setting choices closed the locality loophole. The result, $S = 2.42 \pm 0.20$ , violated the bound of $2$ while closing the locality and detection loopholes together. Photonic experiments (Giustina et al.; Shalm et al.) reached the same conclusion the same year with high-efficiency detectors.

What remains

No experiment can ever close the superdeterminism / measurement-dependence loophole completely: if one denies that settings are freely chosen at all, no test of locality is possible even in principle. Short of that radical stance, the 2015 experiments establish that Nature genuinely violates Bell inequalities — local realism is refuted by experiment, not just by argument.

The takeaway

The three closable loopholes — locality, detection, and freedom-of-choice — each offered a local model an escape. The 2015 loophole-free tests shut all three at once, turning Bell's theorem from a theoretical no-go into an experimental fact, and making device-independent protocols physically sound.