Dear List members.
I would appreciate if anyone familiar with Bell State Measurements
could answer a question. To clarify, Bell State measurement is when two photons
are made to meet at a half silvered mirror at the same time. Two detecters are
set up which will detect the photons whether they are reflected or not. The
probability of reflection or non reflection is . 5. There would seem to be four
possibilities
Possibility 1
Photon x reflected detected in detecter Y
Photon y not reflected detected in detecter Y
Possibility 2
Photon x not reflected detected in detecter X
Photon y reflected detected in detecter X
Possibility 3
Photon x reflected detected in detecter Y
Photon y reflected detected in detecter X
Possibility 4
Photon x not reflected detected in X
Photon y not reflected detected in Y
Possibility 3 and possibility 4 are indistinguishable and put the two photons
in an entangled state. Here's my question. It seems obvious that with this
arrangement the probability that the two photons will become entangled should be
. 5. However it is not. It is actually . 25. Could someone explain why this
is so?