[axilmar]

> Victor can prepare a pair of quantum particles in a special state known as an entangled state. In this state, the outcomes of Alice's and Bob's measurements are not just random but are correlated in a way that defies any classical explanation based on local hidden variables.

What if there are no hidden properties per particle, but the combination of specific property values of particles allow for breaking Bell's Inequality?

I.e. what we call 'entanglement', it might not be 'action-at-a-distance', but the simple effect of the interaction of the properties of the two particles as they are generated.

For example, if we have two billiard balls, which are really close together, and we hit them with a third ball simultaneously, their spin will be correlated when we measure it for both balls (without taking into account other factors, i.e. friction, tilting of the table etc). Wouldn't that break Bell's inequality as well? the spins of the two balls will be correlated.

[Maro]

"their spin will be correlated" - in this case the billiard's spin is a per-ball property that is set before they are sent to Alice and Bob, and happens to be correlated. You can simulate this in the Python code, but you will not be able to break the Bell inequality like that. This is similar to the dice example I give, where the objects sent to Alice and Bob are random from their perspective (since the dice roll happens with Victor), and correlated.

In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices]. To be clear, I didn't prove this in the article, the approach the article takes is "here is some code, play around with it to get a feeling for why".

Hope this helps.

[axilmar]

> In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices].

What if the particles have properties that mutate their state after they are sent to Alice and Bob?

Suppose, in the billiards example, that I put a small device into the balls that changes the spin of the ball to some predefined value.

Wouldn't that break the Bell inequalities without action at a distance?

The reason for the breaking would be that the state of the balls would be modified after they are sent to Alice and Bob. It would look like action at a distance without being 'action at a distance'.

[Maro]

It doesn't matter when the state of the ball changes (when Victor sends them, on the way, when it's measured). You can play around with this in the Python code, there is shows up like "it doesn't matter which function you put that line of code, the functions are called one after the other". The functions in question are generate_composite(), split(), and the 4 measure_X_Y(), called from bell_experiment().