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1/ Here is a proposal of how to distinguish between different, supposedly "equivalent," #orthogonal mixtures of photons. In this case, it is R + L mix of circular, to be distinguished from mixtures of linear #polarization.
#Physics #QuantumMechanics #ThoughtExperiment
I am leaving aside right here whether it could lead to #FTL communication (#SuperluminalSignalling), and focusing on the bare being able to make the distinction. Impractical - but of major theoretical importance.
#ProperMixtures #MeasurementProblem
We use a compound detector D for this purpose. Its first element is a quarter-wave plate with horizontal fast axis, that is rotationally free within a small angle (to allow measurement of changes in #angularmomentum of roughly a few hundred ħ, which is still very tiny.)
The QWP is paired with a subsequent fixed linear filter set at 135°. Hence the full apparatus is a "R state detector," because an entering RH state is converted to 135° and then passes the linear filter. If a random orthogonal mixture of RH and LH are directed at D,
in the long term half will pass (although converted into linear!) and half will not. Sometimes there will be a "run" like a run of heads in coin toss, of say, many "RH" hits in a row (or mostly RH.) If we examine the change in angular momentum of the QWP, we could find it
increased by nħ or nearly, because of the conversion of n RH states to linear etc. Although we can't really measure a single increment, we can thereby imagine that each photon pass increments the AM of the plate by ħ.
   On the other hand, suppose a mix of diagonal linear
(45° and 135° ) is sent to D. The 45° will be made into RH, and the 135° be made into LH. Either of these has a 50:50 random chance of passing LF. If there is a run of many passes, that run has no clear connection anymore to which circular state happened to pass the LF or to
which linear state entered the QWP. Hence this time, the run will not show the significant change in angular momentum of the QWP. Hence, we could distinguish between the two types of supposedly #equivalentmixtures.
Here, I am setting aside the issue of whether we could use this for FTL communication. In any case, it would be difficult because of 1. difficult measurement of tiny changes in angular momentum and 2. making statistical inferences from very improbable runs of certain hits.
And, those two trade off against each other. Still, of theoretical interest, and related to #NickHerbert's original FLASH idea of years ago.
The situation is quite interesting as a way to break away from simple full-ensemble thinking, and start considering the implications of
exceptional "runs" etc. In this case we tricked the prohibition against distinguishing between 50:50 orthogonal mixtures, by selecting out rare subsets that are very much NOT 50:50 mixes. The idea of subset selection in #experiments of this kind, and to measure
both spin transfer and other aspects of polarization, surely deserves more attention and study regardless of just how the implications pan out.
- readers, please RT the intro tweet if you think your followers might be interested. Thanks!
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