Do any Bell papers plot raw data for non-entangled controls?

[tbp_Wallbreaker]

I've been looking closely at the experimental setups for loophole-free CHSH tests, and there's a methodological detail that's bugging me regarding how baseline calibrations rule out hardware artifacts.

Mathematically, we know the local hidden variable bound is |S| ≤ 2. But from a purely metrological standpoint, how do experimentalists actually prove that a measured S → 2.828 is 100% down to quantum entanglement, and not some unmapped systemic bias or artifact in the tabletop apparatus itself? I'm thinking about things like alignment errors, phase-matching cross-talk in the SPDC crystal, or subtle polarization-angle symmetries in the optical path.

The math gives us a theoretical baseline, sure, but one shouldn't just assume the physical outcome of a control group based on the theory you are trying to test. Is it standard practice in the lab to do a control run where the SPDC source is tuned to a non-entangled product state (like parallel or orthogonal polarization mixtures, the kind of classical photon pairs assumed in CH74/CHSH models) just to map the hardware's baseline response on the coincidence counters?

Specifically, are there any foundational or modern peer-reviewed papers that explicitly plot the raw data profiles of these non-entangled, polarization-correlated control runs alongside the entangled ones? If the consensus is that a physical control run is redundant, how is the hardware structurally isolated from classical geometric or polarization-stream biases driving the baseline above 2 (or 0 in CH74) without an actual classical run to prove it?

I'd really appreciate any insights into the lab methodology or literature references on how these baselines are verified. Thanks.

 

[zonde]

Mathematically, we know the local hidden variable bound is |S| ≤ 2. But from a purely metrological standpoint, how do experimentalists actually prove that a measured S → 2.828 is 100% down to quantum entanglement, and not some unmapped systemic bias or artifact in the tabletop apparatus itself? I'm thinking about things like alignment errors, phase-matching cross-talk in the SPDC crystal, or subtle polarization-angle symmetries in the optical path.

Experimentalists can't prove what you are asking for. Proving is for mathematicians. But there certainly are things that experimentalists have to consider especially when testing a no-go theorem.
I would suggest reading about actual loopholes that experimentalist try to work around: locality loophole, detection or fair-sampling loophole, coincidence time loophole.

The math gives us a theoretical baseline, sure, but one shouldn't just assume the physical outcome of a control group based on the theory you are trying to test. Is it standard practice in the lab to do a control run where the SPDC source is tuned to a non-entangled product state (like parallel or orthogonal polarization mixtures, the kind of classical photon pairs assumed in CH74/CHSH models) just to map the hardware's baseline response on the coincidence counters?

Bell inequalities do not depend on QM. So you are not assuming QM is right when testing Bell inequalities.
But if you mean whether experimentalists check if non-entangled product state can violate Bell states, then I guess no. They rather try to close loopholes.

Specifically, are there any foundational or modern peer-reviewed papers that explicitly plot the raw data profiles of these non-entangled, polarization-correlated control runs alongside the entangled ones? If the consensus is that a physical control run is redundant, how is the hardware structurally isolated from classical geometric or polarization-stream biases driving the baseline above 2 (or 0 in CH74) without an actual classical run to prove it?

Experimentalists do not prove statements. They test if statements match observations.
But if you mean how do we know that classical process can't exceed baseline above 2 then this is can be modeled without actual experiments using our experience about how reality works.

 

[.Scott]

I've been looking closely at the experimental setups for loophole-free CHSH tests, and there's a methodological detail that's bugging me regarding how baseline calibrations rule out hardware artifacts.

Mathematically, we know the local hidden variable bound is |S| ≤ 2. But from a purely metrological standpoint, how do experimentalists actually prove that a measured S → 2.828 is 100% down to quantum entanglement, and not some unmapped systemic bias or artifact in the tabletop apparatus itself? I'm thinking about things like alignment errors, phase-matching cross-talk in the SPDC crystal, or subtle polarization-angle symmetries in the optical path.

Most of the loopholes that concern Bell-test experimenters focus on making the measurements space-like.

But there is one kind of error related to the equipment that could result in |S| > 2 results.
It is called the "fair sampling" loophole. When I first read through the Bell Test logic (decades ago), I was immediately struck by this possibility. All you need are photons with hidden values and detectors that are more efficient at detecting when the photons are best aligned with the detector and you will get |S| > 2 results from a purely classical model.

But, in the intervening decades, the detection efficiencies in some experiments have improved.
The CSHS tests need about 83% detection efficiency to close the "fair sampling" loop hole.
One such experiment is the 2015 NIST experiment as reported in APS. In that experiment, the detection efficiency was about is reported to be 91 +/- 2%. That's ample to close the loophole.

Because the basic cause of equipment issues are the result of classical processes, equipment issues that do not effect the sampling would either have no effect on |S|, or tend to make it lower. In other words, the goal is not to prove that there are no classical methods at work, but to demonstrate that some part of the mechanism must be non-classical.

The primary purpose of these "loophole-free" Bell Tests are not designed to measure the |S| precisely. But only to demonstrate that the experimental results cannot be explained through purely local mechanics.

 

[tbp_Wallbreaker]

Most of the loopholes that concern Bell-test experimenters focus on making the measurements space-like.

But there is one kind of error related to the equipment that could result in |S| > 2 results.
It is called the "fair sampling" loophole. When I first read through the Bell Test logic (decades ago), I was immediately struck by this possibility. All you need are photons with hidden values and detectors that are more efficient at detecting when the photons are best aligned with the detector and you will get |S| > 2 results from a purely classical model.

But, in the intervening decades, the detection efficiencies in some experiments have improved.
The CSHS tests need about 83% detection efficiency to close the "fair sampling" loop hole.
One such experiment is the 2015 NIST experiment as reported in APS. In that experiment, the detection efficiency was about is reported to be 91 +/- 2%. That's ample to close the loophole.

Because the basic cause of equipment issues are the result of classical processes, equipment issues that do not effect the sampling would either have no effect on |S|, or tend to make it lower. In other words, the goal is not to prove that there are no classical methods at work, but to demonstrate that some part of the mechanism must be non-classical.

The primary purpose of these "loophole-free" Bell Tests are not designed to measure the |S| precisely. But only to demonstrate that the experimental results cannot be explained through purely local mechanics.

I really appreciate your comment, especially your historical insight into the fair-sampling loophole. You accurately diagnosed how a classical state can exploit hardware detection profiles to fake a violation.

However, invoking the 91% detection efficiency of the 2015 NIST experiment still shifts the question from an empirical control to a mathematical deduction. High efficiency closes the specific particle-dropping loophole modeled by Bell, but it still does not substitute for a physical negative control run on that exact same hardware.

My metrological question remains: Did the NIST team actually tune their SPDC source to an unentangled, polarization-correlated product state and plot that empirical baseline to prove the 91% efficient apparatus strictly defaults to |S| ≤ 2 under classical input? Or did they rely on the mathematical certainty of the 83% threshold to bypass the physical control run entirely?

If the latter, it remains a theoretical presumption rather than an empirically isolated hardware test.

(And fully agree—nothing beats a good night's sleep!)

 

[Matterwave]

Have you already looked through papers and didn't find what you were looking for? It might be helpful to state which papers you already read.

It is standard practice that in experimental papers care is taken when it comes to possible systematic errors. Sometimes the detailed analyses get pushed to appendices though.

 

[PeterDonis]

Did the NIST team actually tune their SPDC source to an unentangled, polarization-correlated product state

This isn't possible; that's not how SPDC works. Either you get a pair of entangled photons triggered by the input "pump" photon, or you just get the "pump" photon passing through the apparatus and doing nothing. You can't "tune" the apparatus to pick whether you get pairs of entangled photons or pairs of unentangled photons.

https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

 

[tbp_Wallbreaker]

Have you already looked through papers and didn't find what you were looking for? It might be helpful to state which papers you already read.

It is standard practice that in experimental papers care is taken when it comes to possible systematic errors. Sometimes the detailed analyses get pushed to appendices though.

I have spent considerable time digging through foundational papers and supplementary materials, and have yet to find a single published plot of a physical LHV/product-state run on the exact same apparatus.

Since you are a Science Advisor and have access to the literature, perhaps you could simply point me to one? If it’s standard practice and embedded in the appendices of a prominent paper (like Aspect or NIST), a simple citation or figure number would completely resolve my inquiry. That is exactly what I am here asking for.

 

[tbp_Wallbreaker]

This isn't possible; that's not how SPDC works. Either you get a pair of entangled photons triggered by the input "pump" photon, or you just get the "pump" photon passing through the apparatus and doing nothing. You can't "tune" the apparatus to pick whether you get pairs of entangled photons or pairs of unentangled photons.

https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

With respect, that is not how SPDC physics works. In Type-II SPDC, the output photons naturally emerge in two polarization-orthogonal cones as a product state. Polarization entanglement is only achieved at the specific intersection lines of those cones where spatial mode indistinguishability is enforced.

Experimentalists can easily collect single modes outside these intersections or alter the pump to generate non-entangled, polarization-correlated pairs on the exact same tabletop setup. My question remains focused on whether data for such non-entangled, polarization-correlated runs has been published as an empirical baseline.

 

[.Scott]

Experimentalists can easily collect single modes outside these intersections or alter the pump to generate non-entangled, polarization-correlated pairs on the exact same tabletop setup. My question remains focused on whether data for such non-entangled, polarization-correlated runs has been published as an empirical baseline.

And that would result in |S| ≤ 2 statistics. So they must have gotten that right.

 

[PeterDonis]

Experimentalists can easily collect single modes outside these intersections or alter the pump to generate non-entangled, polarization-correlated pairs on the exact same tabletop setup.

Can you give specific references for these statements?

 

[Matterwave]

I have spent considerable time digging through foundational papers and supplementary materials, and have yet to find a single published plot of a physical LHV/product-state run on the exact same apparatus.

Well I was responding to your general request, which seemed to me to be how to control for systematic errors and noise.

If this single plot is all you're looking for, does figure 2 in this paper work for you: https://arxiv.org/abs/quant-ph/0511265

It's published in PRA: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.73.062110

It's tuning a param to go from a mixture of product states to an entangled state.

Since you are a Science Advisor and have access to the literature, perhaps you could simply point me to one? If it’s standard practice and embedded in the appendices of a prominent paper (like Aspect or NIST), a simple citation or figure number would completely resolve my inquiry. That is exactly what I am here asking for.

Being a science advisor doesn't give me any special access to journals / papers. I have to search and read like everyone else. It would be a nice perk to have though, ngl...

 

[tbp_Wallbreaker]

Well I was responding to your general request, which seemed to me to be how to control for systematic errors and noise.

If this single plot is all you're looking for, does figure 2 in this paper work for you: https://arxiv.org/abs/quant-ph/0511265

It's published in PRA: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.73.062110

It's tuning a param to go from a mixture of product states to an entangled state.


Being a science advisor doesn't give me any special access to journals / papers. I have to search and read like everyone else. It would be a nice perk to have though, ngl...

Nice to see you dug up the 2006 PRA paper - Fig 2 is really beautiful, but it slightly misses the mark from a data perspective.

The "coloured noise" they injected via timing compensation is actually a dephased quantum state, not a true LHV mixture. It tracks how much quantum perturbation the system can take before the violation collapses, instead of serving as a pure classical negative control.

What I'm looking for is a strictly classical benchmark—running the exact same hardware on a pure LHV state where photon pairs are pre-determined as parallel or orthogonal at emission (a classical statistical mixture like $|H,H>$ or $|V,V>$, completely devoid of quantum superposition).

 

[Matterwave]

What I'm looking for is a strictly classical benchmark—running the exact same hardware on a pure LHV state where photon pairs are pre-determined as parallel or orthogonal at emission (a classical statistical mixture like $|H,H>$ or $|V,V>$, completely devoid of quantum superposition).

I don't understand this objection. If you plug in $p=0$ into equation 1 you get $\rho_C=\frac{1}{2}(|o_1\rangle|o_2\rangle\langle o_1|\langle o_2|+|e_1\rangle|e_2\rangle\langle e_1|\langle e_2|)$ which looks like a mixture of product states to me.

 

[tbp_Wallbreaker]

I don't understand this objection. If you plug in $p=0$ into equation 1 you get $\rho_C=\frac{1}{2}(|o_1\rangle|o_2\rangle\langle o_1|\langle o_2|+|e_1\rangle|e_2\rangle\langle e_1|\langle e_2|)$ which looks like a mixture of product states to me.

Plugging p = 0 is just algebraic extrapolation—like inspecting an AI model weights at a theoretical limit rather than a zero-shot test on real hardware. Did they actually load the state and plot the raw counts, or just assume the theory holds? As René Descartes says, we must doubt everything until it is physically proven. Do you agree too?