How fast is quantum entanglement? Scientists investigate it at attosecond scale

We just call it the "speed of light" because it's the speed that massless particles (like photons) travel at in a vacuum.

Supra-luminal signals will almost necessarily imply that it's possible to violate causality by arranging a series of supra-luminal communications. Not every supra-luminal communication violates causality, but it's hard to think of a way to build a consistent theory that would both preclude causality violations and permit at least some supra-luminal signaling.

It's not possible to use entanglement to transmit information faster than light, even though the entanglement itself could be simultaneous.

To be a reasonable analogy it has to capture something this is different between entangled and not entangled particles. That's the thing that is sometimes described as "spooky" and completely missing from the split coin analogy.

Suppose you did CHSH but instead of pairs of entangled photons with was pairs of non-entangled photons that were polarized in the same direction. They players do the same thing as with entangled photons: use the bit from the referee to pick their measurement angle. A measures at 0 or 45 degrees, where 0 is the axis the photons were polarized on. B measures at -22.5 or 22.5.

Let's say the 0 degrees the players are using is the direction of the original polarization axes.

When the referee gives a 0 to A then A is measuring on the same axis the photon was polarized on, so will get a 1. When the referee gives a 1 to A then A measures at 45 and Malus gives a 50/50 chance of 1.

Player B is always measuring 22.5 from 0, so Malus says B gets a 1 85% of the time.

That gives us this:

  Ref A    Ref B     A's 1/0 chances   B's 1/0 chances
    0        0          100/0                85/15
    0        1          100/0                85/15
    1        0          50/50                85/15
    1        1          50/50                85/15

If the player's setup isn't aligned with the initial axis the result will differ. For example let's say their set up is 10 degrees off from the setup described above. Then their angles are 10 and 55 for A and -12.5 and 32.5 for B. If I did the numbers right they will win around 62% of the time.

Without entanglement when each player measures a photon the θ for Malus's law is the angle between the axis they measure and the axis the photon was originally polarized with.

With entanglement the θ is the angle between the two axis that the players used.

You can play around with this by trying to design the pair of devices that were described in my second link (https://news.ycombinator.com/item?id=35905284).

To recap, you want to design a pair of devices that each have 3 buttons labeled A, B, and C, a red LED, a green LED, and a counter. The counter starts at 1000. When you press any one of the buttons one of the LEDs flashes and the counter decrements. When the counter reaches 0 the device stops responding.

You should also specify a way that if the devices are brought together the pair of them can be reset.

You can specify any kind of non-quantum hardware you want in the devices. As much computing as you need, as much RAM and ROM and disk as you want, and physical sensors. Include clocks if you need to. You can include true random number generators. It doesn't have to be limited to current technology--it just has to be limited to known physics and not use quantum entanglement.

What are need to achieve with that hardware and whatever algorithms you specify is:

1. Suppose someone has used one of the devices, and recorded the results of a very large number of interactions.

Suppose that a statistician is given a list of 5-tuples (P, F, n, R, t) of those interactions with one of the devices, where P is which button was pressed, F is which LED flashed, n is the value on the counter when the button was pressed, and R is how many times the device has been reset (i.e., R = 0 the first 1000 times the device is used, then when it and the other device are reset R = 1 for the next 1000 uses and so on), and finally t is the time at which the button was pressed.

It should not be possible using any known statistical test on that list of 5-tuples for the statistician to distinguish the device from a device whose algorithm is simply:

  if any_button_pressed():
    r = uniform_true_random_from_0_to_1()
    if r < 0.5:
      flash(GREEN)
    else:
      flash(RED)

A couple things to note.

1. The above has to hold even if the users take the devices very far apart from each other before they start pressing buttons.

In particular the users might choose to take the devices so far apart before they start pressing buttons that each has finished their run of 1000 before any possible communications from their device could reach the other.

2. The users might wait a long time before starting a run of 1000, and they might wait a long time between presses within a run.

3. The users are determining when to press independently so you can't count on them alternating. You can't even count on them overlapping: one might do all 1000 presses before user the other starts.

4. The users might use a true random number generator to determine which buttons to press.