# Sample Experiments – Polarisation Entanglement – Violating Bell’s Inequality (CHSH)

The definition of an entangled state in quantum physics can be rather simple: It says two quantum objects cannot be described separately anymore, only together.

If one wants to show that a quantum system is entangled, usually a so-called “Bell inequality” is employed. In the case of polarisation entangled photon pairs (as emitted from the quED), the so-called “CHSH” inequality is often chosen.

Classical (“local realistic”) theories predict that a certain value “S” has an upper bound of 2 (meaning S<=2). When quantum theory is used to calculate the corresponding value, S can exceed a value of 2, the new bound is 2*sqrt(2).

Practically, the S value is determined by measuring the coincidence count rate at 16 different polariser settings and adding and subtracting these values. So, we put one polariser in each arm: The quCR software helps you with the measurements and outputs the S value and the amount of standard deviations (n) the Bell inequality has been violated by. We said that any S value above 2 shows it is an entangled state. Here we measured S=2.7, so the state is well entangled.

What happens if we put in a non-entangled (=separable) state? We can produce such a state with the quED when we remove the wave plate in the pump beam. (I.e. switch off the pump laser, open the round lid of the white pump beam box, remove the wave plate from the beam, put the lid back on and switch on the laser.)

This is what we have measured: The measured S value is 1.647, which is well below 2.

What does this S value mean? Is this state entangled or not? Can it be explained by local-realistic theories?

#### What do you need?

• 1 x quED (motorised version advised for demonstrations)