Quantum challenge: How to distinguish H and V pol from diagonal mix - using long spatial separation of components
- From: "Neil B." <neil_delver@xxxxxxxxxxxxxxx>
- Date: Fri, 2 Jan 2009 12:14:11 -0500
There is a way in principle IMHO to distinguish H and V polarization
from diagonal mix - using spatial separation of components. I'm not
sure how practical it would be to find the difference, but it's worth
looking into and I believe this is an original proposal. I thought of
it some years ago but haven't put it out before.
It is commonly held (density matrix formalism and standard quantum
information theory) that there is no way to distinguish equivalent
mixtures. An example would be, mix of H and V pol. light from mix of
diagonals. In terms of the fundamentals of projection (statistics of
filters for basis states, etc.) it can be shown, there isn't any way
to tell the difference - but that is based on simplistically assuming
a certain context that doesn't have to apply. Such assumptions are
forgivable as useful ways to get the basics down, but they narrow
attention away from thinking "outside the box." That OOTB thinking can
be applied to the current question.
Consider that linear birefringent materials work by delaying one wave
component relative to the orthogonal one. Hence if the component
parallel to the slow axis is delayed by a half cycle relative to the
fast axis, we have a half-wave "retarder" plate that can do things like
change the angle or rotational sense of polarized light. BTW these are
not "filters" since they don't absorb any components. There is nothing
to stop us making a long retarder imposing a delay of many wavelengths,
or even beyond the coherence length of the photon (IOW, more than the
millions or so cycles that make up the pulse packet of the photon, the
length determined e.g. by emission time such as 10^-8 s.)
We should be able to use such a long retarder to distinguish mixes of H
and V from diagonals. Set the LR's axes to be fast x and slow y (H and
V). Nothing special happens when either an H or V photon goes through,
except for overall delay: so the mix is basically of the same sort of
objects as before. But if a diagonal photon goes through (superposition
that's either of 0.5(sqrt 2)(|x> +/- |y>)) then the y component is
held way behind the x component. That is enough to make a doubly peaked
photon that is very weird: the front end wave amplitude is actually
oriented along the x axis and the rear end, separated by an essentially
flat region, is actually oriented along the y axis. IMHO this presents
an opportunity for making a distinction. The simple behavior of
idealized filters in basic quantum theory might still not allow a
distinction, but we are not limited to that. We have access to various
forms of non-linear optics, choppers that might allow filtering or
selecting the front and back ends in different ways, use of PEMs
("photoelastic modulators" can change polarization very rapidly and
should be more in the news), interference schemes that combine the
separated peaks in unusual ways, etc. Some such applications might be
able to show the polarization distinction in a creative way. Even
though
I'm musing over just how to do this there aren't details here, it's just
put out to see what others can come up with.
If we can distinguish such mixtures (against the prediction of standard
quantum theory) then the implications may be profound. It certainly
changes what is possible in quantum information and communication. Some
would say, it might allow FTL signaling (depending on one's
interpretation of how entanglement works and what photon state "is
really there" before a measurement.) The basic quantum picture of how
things are constructed of superposed states wouldn't change, however,
instead some subtle implications with possible applications.
Neil Bates
.
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