Understanding Properties of the Entangled Photon Ψ+ Bell State

|Ψ⁺⟩ Bell State Property 1.1:  The polarization state of an individual photon cannot be predicted for either idler or signal

|Ψ⁺⟩ Bell State Property 2.1:  IF the linear polarizer at idler is perpendicular to (rotated 90 degrees with respect to) signal, THEN the same detector at idler and signal will register a photon at the same time.  The IF, THEN statements can be reversed between signal and idler as this is temporally symmetric with no causal order.

|Ψ⁺⟩ Bell State Property 2.2:  IF the linear polarizer at idler is parallel to signal, THEN the opposite detector at idler and signal will register a photon at the same time. The IF, THEN statements can be reversed between signal and idler as this is temporally symmetric with no causal order.

|Ψ⁺⟩ Bell State Property 2.3:  2.1 and 2.2 are true for any pair of perpendicular and parallel linear polarizations of idler and signal

|Ψ⁺⟩ Bell State Property 3:  IF the linear polarizer at idler is rotated 45⁰ to signal, THEN the opposite idler and signal detectors will register half of the time and the same detectors will register half of the time. The IF, THEN statements can be reversed between signal and idler as this is temporally symmetric with no causal order. This is true for any pair of signal and idler linear polarizers that differ by 45⁰.