# Bell inequality violated with classical light in experiment

1. Aug 18, 2015

### DirkMan

https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-2-7-611&id=321243

"In our experimental test, we used light whose statistical behavior (field second-order statistics) is indistinguishable from classical, viz., the light from a broadband laser diode operating below threshold. Our detections of whole-beam intensity are free of the heralding requirements familiar in paired-photon CHSH experiments. Repeated tests confirmed that such a field can strongly violate the CHSH Bell inequality and can attain Bell-violating levels of correlation similar to those found in tests of maximally entangled quantum systems."

I thought bell's inequalities cant be violated by classical things ?

2. Aug 18, 2015

### votingmachine

Perhaps. Their final comment is to that effect:

3. Aug 18, 2015

### atyy

Maybe the paper is wrong. It's probably like papers that violate energy conservation - they have to be wrong - even if you cannot immediately find the error.

If they do violate a Bell inequality, they will have to take one of the outs like free will.

4. Aug 18, 2015

### morrobay

5. Aug 19, 2015

### Jazzdude

I've just finished reading the linked paper's sections 1, 2 and 7. Those are introduction, theoretical background and summary/interpretation and all you need to understand the basic idea of the paper and what they are really doing.

The paper's main feature is not anything revolutionary, but rather ordinary obfuscation and complication of simple things and the only astounding aspect is, that the authors managed to get confused regarding the meaning of their own arbitrary theoretical constructions. And I can say, I wholeheartedly disagree with their interpretation and conclusion.

They start by writing down a general form for the electric field of a polarised light beam at the position of a detector:
$$E(t) = E_x(t)\cdot \hat{x} + E_y(t)\cdot \hat{y}$$
and demand the light be entirely unpolarised and intensity normalised, meaning $\langle E_x(t), E_y(t) \rangle=0$ and $\langle E_x(t),E_x(t)\rangle=\langle E_y(t),E_y(t)\rangle=1$.

Their next step is the important one, when they claim that this state can be regarded as an entangled state between polarisation and amplitude degrees of freedom, as it cannot be written as a product in the form of $$E(t) = E_u(t)\cdot\hat{u}$$ for a constant direction $\hat{u}$.

This is of course true, but arbitrary and misleading. First of all, they assign the time dependence arbitrarily to the amplitude state and not the direction state. It is only that choice that generates the inseparability and allows them to call this state entangled. Second, entanglement is usually used as a descriptive property of a state and not a history. The inclusion of time in the space they consider is very misleading and does not allow for any comparison with the Bell setup. And finally, their "entangled" classical state is fully localised spatially at the detector. To violate the Bell inequalities in a meaningful way, you have to eliminate the causal channel from the setup.

Given these flaws, their conclusion sounds extremely far fetched and in my eyes even wrong. They have not demonstrated the violation of the Bell inequalities in a setup that would deserve the name. They merely show, experimentally, a simple fact that can be derived easily mathematically and is in absolute agreement with classical electrodynamics or even just basic statistics. Anybody who really understands Bell should not find that result exciting nor surprising and it is certainly not redefining anything, and in particular not the quantum classical boundary.

Cheers,

Jazz (who is quite disappointed with the quality of the majority of papers published these days)

Last edited: Aug 19, 2015