Loophole-free Bell tests reported in 2015

Short answer: In 2015 three groups reported Bell tests that closed the most significant loopholes at once. One used entangled electron spins 1.3 kilometres apart (Nature), and two used entangled photons (Physical Review Letters, published 16 December 2015). Each reports rejecting local realism, with statistical strength that differs a lot between the experiments. These are laboratory physics results.

What a loophole is

The Nature paper recalls that John Bell proved no theory obeying locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, correlations between outcomes on distant particles satisfy an inequality that entangled particles can violate. The authors say all earlier experiments required additional assumptions to reach a contradiction with local realism, leaving loopholes.

One Physical Review Letters paper (article 250401) describes the fair-sampling or detection loophole: under local realism it is conceivable that a subensemble of emitted particles violates a Bell inequality while the total ensemble does not, and an experiment exploits this if it detects only that subensemble and assumes it represents everything. It says the loophole can be closed by detecting particles with adequate efficiency. The same paper says the long-term goal has been to close all loopholes in a single experiment.

Electron spins, 1.3 kilometres apart

The Nature authors report a Bell experiment they say is free of any such additional assumption. They use an event-ready scheme to generate entanglement between distant electron spins, with an estimated state fidelity of 0.92 plus or minus 0.03. Efficient spin read-out avoids the fair-sampling assumption, and fast random-basis selection and read-out combined with a 1.3 kilometre separation ensure the locality conditions.

They performed 245 trials of the CHSH-Bell inequality and found S = 2.42 plus or minus 0.20, where local-realist models give S of at most 2. A null-hypothesis test gives a probability of at most P = 0.039 that a local-realist model could produce a violation at least this large, even allowing for memory in the devices. The authors conclude their data imply statistically significant rejection of local realism.

Two photon experiments

The first photon paper (Physical Review Letters 115, 250402, titled Strong Loophole-Free Test of Local Realism) uses entangled photon pairs. The authors ensure all relevant events are spacelike separated by placing the parties far apart and using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source with high-efficiency, low-noise single-photon detectors lets them measure without fair-sampling assumptions. They estimate how well a local realistic system could predict their measurement choices, account for it, and reject the hypothesis that local realism governs the experiment.

The second photon paper (250401) reports a Bell test that closes the most significant loopholes simultaneously, using a well-optimized source of entangled photons, rapid setting generation and highly efficient superconducting detectors. The authors say the purely statistical probability of their results under local realism is small enough to correspond to an 11.5 standard deviation effect.

Limits

The three experiments differ in strength. The electron-spin result is based on 245 trials and a probability bound of 0.039, while the second photon paper reports an 11.5 standard deviation effect. The abstract of the first photon paper does not state its exact values in the text available here, so none are given. The second photon paper says it closes the most significant loopholes, which is not the same wording as the Nature paper's claim of freedom from any additional assumption.

FAQ

What did the Nature experiment use?

Entangled electron spins separated by 1.3 kilometres, with an event-ready scheme and fast random-basis selection and read-out.

How significant was the electron-spin result?

S = 2.42 plus or minus 0.20 from 245 trials, with a probability of at most P = 0.039 for a local-realist model, according to the authors.

What was reported with photons?

Two papers published 16 December 2015 in Physical Review Letters report violations using entangled photon pairs, high-efficiency detectors and fast random settings. One reports an 11.5 standard deviation effect.

What is the fair-sampling loophole?

It is the possibility that only a subensemble that violates the inequality is detected while the total ensemble does not.

Do these tests use the same loophole closures?

Each paper describes its own approach. The papers describe closing the detection and locality loopholes, and one says three tests together remove the last doubts that local realism must be renounced, which is that paper's own framing.