Detection Loophole, Minimum Percent

[James Jr Tankersley]

Even though we know how to close the detection loophole with electron spin experiments, photon-based experiments are still being used to test Bell's inequalities, without properly closing the detection loophole (Eberhart requires 72.5% detection, but CHSH simulations modeling Malus law loss at the polarizing beam splitter appears to require detection closer to 100% to close the detection loophole)

A recent paper cites 3 Bell tests in 2015 (2 photon based with ~75% detection rates) as being loophole free. [1]. A recent Nova documentary also cites a recent Vienna photon based experiment [4.1] as being loophole free.

The 2015 Electron spin experiment is loophole free as far as we know (Hensen et al, with 100% detection), but has not been repeated in almost a decade, as far as I can determine, and the published run was apparently only 245 events, with a high probability of being a random chance result [1] (1 in 27) [5].  

If future Electron spin experiments with sufficient trial data refute the tiny trial run above, we appear to have something interesting (but no similar experiments in this many years???)

Eberhart is cited as requiring a minimum of 72.5% detection rate to avoid detection loop hole. (Now achievable with high quality photon detectors)

However, Eberhart's minimum detection must assume a "random distribution" of photon loss, not the "highly selective" loss Malus law causes to photons with real polarities before entering polarizing beam splitters (which very selectively lose photons based on pre-existing photon polarization).[3] 

CHSH simulations of photon with real polarities before hitting polarizing beam splitters, modeling loss using Malus Law calculations, show S violations around 2.2 when detection efficiency is modeled at around 90%[2]. The detection rate needed to close the loophole may need to be closer to 100%, based on the numbers the simulations are providing.

Cheers,

Jim Tankersley

(usually busy with work, but recently inspired by recent events)

[1] LOOPHOLE-FREE BELL TESTS AND THE FALSIFICATION OF LOCAL REALISM, 2018, https://arxiv.org/pdf/1805.09289.pdf, 2018 (accessed 2023-01-22)

[1.1] Discussion, page 8 "Finally, by using highly efficient detectors and testing a version of the CH model, they were able to close the detection loophole (Shalm et al., 2015). The necessary theoretical efficiency for this experiment, which Shalm et al. calculated using the method proposed by Eberhard, was 72.5% (Eberhard, 1993) (Shalm et al., 2015). The actual detector efficiencies used were 74.7 ± 0.3% and 75.6 ± 0.3% as calculated using the method proposed by Klyshko (Klyshko, 1980) (Shalm et al., 2015)."

[2] Testing Bells Theorem, https://sites.google.com/site/physicschecker/unsettled-physics/testing-bells-theorem-paper (access 2023-01-22)

[3] Malus Law, https://byjus.com/jee/malus-law/ (accessed 2023-01-22)

[3.1] "What is Malus Law?

Malus’ law states that the intensity of plane-polarized light that passes through an analyzer varies as the square of the cosine of the angle between the plane of the polarizer and the transmission axes of the analyzer." 

[4] Einstein's Quantum Riddle, https://www.youtube.com/watch?v=068rdc75mHM (accessed 2023-01-22)

[4.1] Dominik Rauch, University of Vienna (43 minute point)

[5] Quantum Entanglement Bell Tests Part 4: Delft – The 1st Loophole-free Bell Test, Karma Penny, https://www.youtube.com/watch?v=9XHJfUeEmns&t=17s (accessed 2023-01-22)