Challenges and Setup for Bell Inequality Experiments

Bell inequalities, established by physicist John S. Bell, are mathematical conditions that imply the existence of non-local correlations [1] between entangled particles. Experimental results have consistently demonstrated that quantum mechanics’ predictions contradict those of classical mechanics, reinforcing the notion that local realism, or the principle of locality, does not hold in the quantum realm. However, achieving a definitive and unambiguous violation of Bell inequalities in experimental settings poses several challenges.

In this study, the researchers delve into the complexities of conducting Bell violation experiments in quantum mechanics. They aim to decide if the world truly operates as strangely as quantum mechanics suggests, and whether Nature aligns with Einstein’s principle of locality or Bohr’s concept that an object’s properties remain undefined until observed. A Bell test serves as the experimental tool for this investigation.

The main challenges of these experiments are the loopholes, that is, ways in which nature, or an eavesdropper, can arrange experimental outcomes so the experiment appears non-local while in reality it is not. The detection loophole arises because not all emitted particles are detected during the experiments mainly due to inefficient detectors. Even more, the locality loophole is present if measurements are performed such that a subliminal signal can transfer information between measurements stations during a measurement sequence. To address this loophole matter,  scientists have developed high-efficiency detectors and have devised an experimental setup with spacelike separations, such as using distance entangled particles or space-like separated measurements on a single particle. These setups provide stronger evidence against local realism.

Proposed Experimental Techniques and Optimization

To overcome these challenges and push the boundaries of Bell violation experiments, the team, in their study, proposed an experiment utilizing quantum optics techniques and tools such as a two-mode squeezer, displacements, and click detectors (on-off detectors). To begin with, two-mode squeezers are devices that generate entangled photon pairs. Moreover, these squeezed states of light can enhance the precision of a measurement due to techniques that help reduce the shot-noise produced by photons. Specifically, two-mode squeezers generate weakly squeezed two-mode squeezed vacuum states. Consequently, we send half of each state a short distance to an on-off detector, while directing the other half to a distant interferometer.

The choice of measurement settings critically determines whether we observe non-local correlations in this type of experiment. To achieve a conclusive violation of Bell inequalities, the experiment must select measurement settings that guarantee a strong correlation between the entangled particles. The proposed experiment involves multiple parties, each with an independent setting.

This paper investigates how to optimize Bell violation in the proposed experiment. We found that a specific squeezing parameter maximizes the Bell violation. We also analyzed how dark counts influence the experiment’s robustness. At lower dark count rates, achieving a violation of the Bell inequality is easier, but it becomes harder at higher rates.

The proposed experiment leverages the precision of quantum optics tools and shows some promise in addressing the main challenges. A configuration with two-mode squeezers and high-efficiency detectors offers advanced capabilities for generating and measuring entangled photon pairs. We cannot underestimate the impact of experimental imperfections, but we must understand the relations between them and their effects on the Bell inequality violations to interpret experimental results accurately.

Tools for Quantum Optics

Quantum optics tools offer significant advantages. However, imperfections can still impact on the experimental results, some sources of imperfections are:

  1. Dark counts: dark counts refer to false counts in the detectors that occur even in the absence of incident photons. Experiment’s robustness against dark counts depends on the probabilities of it happening. If the dark count is too high it becomes challenging to obtain conclusive results. Advanced detector technologies can be used to mitigate dark counts.
  2. Channel loss: the transmission of entangled photons through optical channels can result in losses due to absorption and scattering. The analysis of the experiment shows that using more parties can make it easier to achieve non-locality even in the presence of channel loss. However, there is a critical transmission threshold beyond which the experiment’s robustness diminishes. This threshold represents a limitation based on the transmission distances.
  3. Phase and amplitude noise: phase and amplitude noise in optical components can introduce errors in the measurements, potentially reducing the strength of the Bell violations. There must be careful control to minimize the sources of noise to maintain the experiment’s accuracy.

Reference: Proposal for a long-distance nonlocality test with entanglement swapping and displacement-based measurements. Anders J. E. Bjerrum, Jonatan B. Brask, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen. Phys. Rev. A 107, 052611 – Published 23 May 2023.

[1] Nonlocal correlations are a quantum phenomenon that constitute a stronger form of correlations than quantum entanglement

Sketch of the analyzed setup with N parties. The left-going modes are labeled Pn, and the right-going modes are labeled Sn. A detector associated with a mode is given the same label as that mode. The measurement performed by the detectors in S effectively swaps the N bipartite entangled states, from the two-mode squeezers, into an N-mode entangled state. “ch” abbreviates channel.


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