Entangled photons – Visualization of the measurement process

When “projected” from the quantum dimension into the three-dimensional world, the rotationally symmetrical oscillation Omega throws two “shadows” to Alice and Bob, describing the probability distributions for transmission (white ring) and reflection (black ring) in every angle of the polarisation rotator. When mapping the rotating wheel to the probability, the phase information is lost, and in turn, one dimension of Omega.

Next, suppose that Alice performs a measurement. What is the impact of Alice’s measurement to Bob?. Alice initially selects her horizontal and vertical measuring axes by an angle of the polarisation rotator determined by her. The angle of Bob’s polarisation rotator is, for the time being, irrelevant to the following discourse.

In the measuring axis selected by Alice, the entangled photon pair Omega interacts with the “White” and “Black” detectors from Alice. Prior to taking the measurement, Omega is, from Alice’s perspective, a superposition of two vertically and two horizontally polarised photons (cf. the red/brown double arrow pairs). For the outcome “White” (□) or “Black” (■), there is always the probability of ½. Prior to taking the measurement, the outcome is not yet certain – the two probabilities are in superposition.

If Alice measures “White” (□) equals transmission, the photon has been vertically polarised in relation to Alice’s measuring axis. When Alice measures “Black” (■) equals reflection, the photon was horizontally polarised. To put it another way: the measurement is the projection of the photon onto either the vertical or the horizontal component at Alice side.
Alice measures again – and her “Black” (■) detector registers a photon, meaning that…
1. the photon measured was horizontally polarised.
2. the vertical portion of the photon pair is destroyed.
3. the remaining photon of the photon pair has the same horizontal direction of polarisation as Alice’s photon.
4. Bob’s oval-shaped probability distribution now describes the observation probability of a horizontally polarised photon.

According to quantum physics, Alice’s choice of her measuring axis has a direct influence on Bob’s potential measurement result, without any time delay. Alice cannot influence whether she obtains the result “Black” or “White”. After taking the measurement, Alice can, however, state with certainty how Bob’s photon will be polarised. However, whether Bob measures Black or White is something that she can only ascertain by comparing the measurement results, as Bob can likewise freely select his measuring axis independent of Alice.