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Someone requested a picture: FYI
Sarfatti quantum connection communication gedankenexperiment



receiver                                   transmitter

p(e')  ------       pair source              ------  e+    _ e^iphi e+
-------|    |   b      ---   a               |    |-------|_|-------\
p(o')  |    |  <--     | |  -->              |    | o- _    o+      |
-------|    |          ---                   |    |---|_|----------__|
       ------                                ------ 1/2 wave
                                                                single
c                                                               counter
       calcite  (angle theta between them)   calcite


p(e') = [1 + sin(2theta)cos(phi - arg<a,e,+|a,o,+>)]/2

p(o') = [1 - sin(2theta)cos(phi - arg<a,e,+|a,o,+>)]/2

p(transmitter counter) = 1

p(e') + p(o') = 1

so local probabilities add to 1 on each side.

The o- 1/2 wave plate and e-phase plate changes entangled pair state

!a,b> = {|a,e,+>|b,e,+> + |a,o,->|b,o.->}/sqrt2

to

|a,b>' = {e^iphi|a,e,+>|b,e,+> + |a,o,+>|b,o.->}/sqrt2

but  |a,o,+> = |a,e,+>e^iarg<a,e,+|a,o,+>

|<a,e,+|a,o,+>| = 1

because the 1/2 wave plate makes |a,e,+> and |a,o,+> have the same
polarization so they are not orthogonal or linearly dependent.

Therefore |a,b>' is disentangled or split into two separate 1-photon states

|a,b>' = |a,e,+> |b>

|b> = {e^iphi|b,e,+> + [e^iarg<a,e,+|a,o,+>]|b,o.->}/sqrt2

p(e') = |<e'|b>|^2

p(o') = |<o'|b>|^2

One can argue that local unitarity for arbitrary 1-photon superpositions
implies

phi - arg<a,e,+|a,o,+> = pi/2

so that the quantum connection signal

p(e') - p(o') = sin(2theta)cos(phi - arg<a,e,+|a,o,+>) = 0

But it is not clear that this argument works for the pair state since

'<a,b|a,b>' = 1

without that condition.

Let experiment decide!