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I try now with some formulas - hope it's reasonably understandable:

First known substance - unless I am floundering in it:

I imagine that the p - photons is measured first (p1) and meets a PBS (0) (x = horizontal and y = vertical). We can then describe the measuring state with regard to polarization by:

k*( lp1,x> ls2,y> + lp1,y> ls2,x> ) - where k = 1 / sqrt (2) (scale factor).

Next s - photons are measured (s2) with a PBS (+45) (+=+45 degrees and - = - 45 degrees).

Change of base: ls2,x> = k*( ls2,+> + ls2,->) and ls2,y> = k*( ls2,+> - ls2,->) and inserted:

k*k*( lp1,x> ( ls2,+> - ls2,->) + lp1,y> ( ls2,+> + ls2,->))

= k * k * (( lp1,x> ls2,+> - lp1,x> ls2,-> + lp1,y> ls2,+> + lp1,y> ls2,->)

= k*(k*( lp1,x> ls2,+> + lp1,y> ls2,+>) + k*(lp1,y> ls2,-> - lp1,x> ls2,->))

There are detectors at 0, 90 and -45 degrees, so that only photons with +45 degrees continues - equivalent to: k*( lp1,x> ls2,+> + lp1,y> ls2,+>)

which corresponds to the expected: that half of the photons continue on + 45 were measured horizontally and half comes from the vertical (at p).

s measured before p: k*( lp2,-> ls1,+> + lp2,+> ls1,->)

Change of base: lp2,+> = k*( lp2,x> + lp2,y>) and lp2,-> = k*( lp2,x> - lp2,y>) and inserted:

k*( k*( lp2,x> - lp2,y>) ls1,+> + k*( lp2,x> + lp2,y>) ls1,->)

Only photons with +45 degrees continues - equivalent to:

k*( lp2,x>ls1,+> - lp2,y> ls1,+>)

a small difference (+ / -) - but measurable would be that half of those who continue will later be measured 'horizontal' and half 'vertical'

And then finally something perhaps not totally trivial?

When the photon passes a PBS changed the reflected photons a half wave = 1/2. No significant change = 0/2. Used entanglement with respect to time, we get:

k*( lp1,x>lp1, 0/2> ls2,y>ls2, 0/2> + lp1,y>lp1, 1/2> ls2,x>ls2, 1/2> )

and the ‘+45’-photons:

k*( lp1,x> lp1, 0/2> ls2,+> ls2, 0/2> + lp1,y> lp1, 1/2> ls2,+> ls2, 1/2>)

So half = the measured 'vertical' - is shifted half-wave

OR

k*( lp2,-> lp2, 0/2> ls1,+> ls1, 0/2> + lp2,+> lp2, 1/2> ls1,-> ls1, 1/2>)

And the ‘+45’-photons now:

k*( lp2,x> lp2, 0/2> ls1,+> ls1, 0/2> - lp2,y> lp2, 0/2> ls1,+> ls1, 0/2>)

So now they are similar with respect to time.

The difference between p1 and p2-s2-s1 should be measurable with a double slit or a suitable interferometer.

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# Entanglement – the order of measurements can be important

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