One concept which Scientists have been working on, is the potential use of quantum entanglement, for communication. And this capability has only been confirmed partially – at best – in the West.
A version of the concept which I once read about, as best as I can remember, was, that a laser generates a pulsed, coherent beam of light, which is next put into a superposed state. And that latter detail means, that the beam is fed through two paths, one ‘direct’, and another which both delayed the light, and phase-shifted it 90⁰. I think that the detail which the article that I had read omitted, was that the superposition was to take place in both these senses simultaneously.
The resulting, superposed beam, can be referred to as a carrier-beam. It was next to be passed through a special crystal, that would split it into two, entangled beams, each of which would also have twice the wavelength of the carrier-beam, due to conservation of energy. Presumably, photons in each resulting beam were to be entangled, with corresponding photons in the other beam. One resulting beam can be called the transmitting-beam, while the other can be called the receiving-beam.
These entangled beams can be passed down two long paths, after which the transmitting-beam can supposedly be modified in a special way, so that the modification can be read out of the receiving-beam. And I think, that the roles of these two beams can be reversed.
Fine. But in order for this to work, there needs to be a way to alter the state of entangled particles – which are originally in a superposed state – so that the states can be witnessed, at least partially, before any measurable difference results in the receiving beam. In order to do that, a component was suggested, the diagram for which looked roughly like this:
The problem with this diagram, is that it can be interpreted in different ways, depending on what we assume to be the fundamental properties of one photon. I’m going set a point of reference – again – that photons are either left-handed or right-handed, because I’ve recently decided they can be so, as an alternative representation of being linearly-polarized.
If we could assume that laser-light which constitutes the signal, had the same (doubled) wavelength as that of the transmitting beam, and if the coherency-length of its laser was greater than the amount of time, by which the photons in the carrier-beam were separated, which were superposed, then the signal ‘could be’ 90⁰ out-of-phase with either of the two superposed photon-states of the transmitting beam.
The signal beam would need to be plane-polarized at an angle, diagonal to the boundary in the component diagrammed above.
What the component visualized above does, is to act as two beam-splitters, which split the transmitting beam as well as the signal. Each time, the beam-splitter is producing two, mutually-perpendicular beams of plane-polarized light. When the light of the transmitting beam mixes with photons of the signal, two beams of circularly-polarized light should result, precisely because the signal would have been 90⁰ out-of-phase with the transmitting beam, regardless of which beam was responsible for the horizontal, or the vertical plane-polarized component, in each case.
So what does that do? Well, according to the first posting I linked to above, if two amplitudes cancel in one specific place, the corresponding particles will not be witnessed – at least at that place. But, because according to one possible state of superposition, a photon is either left-handed or right-handed, either sense of photons will have a wave-function of zero, meaning that either the left-handed or the right-handed photons will not be witnessed.
So potentially, up to 50% of the photons in the transmitting beam will suddenly not be witnessed.
I think there is a relevant observation I should add:
Even though the diagram of this component does not show this, its construction can be asymmetric, but the deflected beams’ phase with respect to time will remain symmetric. When light from one input is plane-polarized perpendicularly to the other beam, the effect would be useful on the transmitting-end, because it would lead to the result that both output-beams would be polarized in the same direction.
If this system was to witness a percentage of the photons, but always with an equal probability of being in either state, then this would not send a useful message to the receiving-end. But, if this system could be made to witness particles at the transmitting-end, always in the same state, then according to what I’ve been told, that number of particles at the receiving-end will assume the opposite state, which can actually be measured, differentially, using a matching beam-splitter / combiner. ( :1 )
The asymmetric beam-splitter I’ve just proposed would also not have its input beams entering at the same angle, because any difference in the dielectric constants would also imply a relative refractive index not equal to one. And so, while the overall geometry can be simplified – with the boundary perpendicular to the apparatus – the angles on one side would be unequal to those on the other side, in a way easy to calculate. In fact, they would correspond to Brewster’s Angle.
And, this signal being 90⁰ out-of-phase with one of the superposed states in the carrier-beam, also means, that it will coincide with the timing of one of those superposed states’ pulses – of which I wrote above, that the 90⁰ phase-shifted state, was also delayed.
And so the format of the exercise could lead to a very practical implementation, because on the receiving beam, the only thing that needs to be done, is that differential changes corresponding to timed pulses, need to be detected.
Now in practice, there is no special reason why the signal would be, exactly 90⁰ out-of-phase, with one of the superposed states. It was generated by an independent laser, and could be in any phase-position. But I also wrote, that the coherency-length of that laser, was supposed to be longer, than the time-delay between the two states of superposition.
What this means, is that regardless of what the phase-position of the signal was, it will be out-of-phase to some degree, with either of the two phase-positions of the superposed states, since no phase-angle can escape two phase-positions that are 90⁰ apart, completely.
I suppose that there’s an observation which I should throw in. The question could be asked, ‘Why does one not simply put a photocell on the receiving beam? Why does the receiving beam also need to have a component as shown above, and with a beam corresponding to the signal at the transmitting-end?’
‘Why does one not construct a simple sensor, sensitive to either left-handed or right-handed light, by first passing the receiving beam through a birefringent crystal, and then through a linear polarizer, which the axes of the birefringent crystal were diagonal to?’
And the answer which I would suggest is, that the relationship between the transmitting and the receiving beam is reciprocal. Even if this does not correspond to the intended sense of how the apparatus is supposed to work, if 100% of particles in the ‘receiving beam’ are witnessed, then this should also set the entangled particles, in the beam intended as the transmitting beam, making the system compromised. In one specific case, the particles would be witnessed, either by the linear polarizer which absorbs them, or by the photocell that follows it.
The use of such a component in the receiving beam, would provide ‘plausible deniability’, about whether either of the superposed states has been witnessed. On that subject, I suspect that in practice, the efficiency of this apparatus would already be compromised – i.e., the amplitude of the signal which can be received diminished – by the mere fact that the component on the receiving beam already witnesses its particles, at a rate of 50%.
When the pulsation of amplitudes – as defined so far – is measured from the receiving beam, it will be evident in the difference between two measured intensities, If the component used for the receiving beam, is asymmetric, as the component was, which I suggested for the transmitting beam. But, because I’ve never owned such an apparatus, I cannot confirm this.
I suppose that somebody could turn around and suggest, that instead of any signal being 90⁰ out-of-phase with one of the superposed states, of the carrier beam, the same beam could be in-phase with the other superposed state of the carrier beam, and that operation based on witnessing linearly-polarized states would result.
My problem with that would be the assumption, as linked to in my blog, that if a polarizing-mirror deflects light plane-polarized in one direction, it transmits light plane-polarized perpendicularly to that one. Thus, as much as I’d like to think that cancellation should take place, I cannot visualize it taking place between two amplitudes, which are also oriented at right angles to each other, regardless of what their phase-position is with respect to time.
And, I cannot visualize that through the addition of two beams, the likelihood of either one’s photons being witnessed would increase, as somebody once suggested to me.
But, by choosing ‘a circular coordinate system’, I may have defined a case where cancellation will occur.
Another issue I could comment on, is at what point the photons count as having been ‘witnessed’. According to some accounts, they are witnessed when a sentient being is made aware of them. I should think that simply being absorbed should cause them to be witnessed ! This would also mean, that if much of the receiving beam was scattered and not received by such a device, all of its photons would eventually be witnessed, and no longer available for manipulation in the transmitting beam.
Further: I’ve just learned to drop from my vocabulary, that a superposition of states
can be made to collapse. However, it still belongs to my vocabulary, that one state of a particle can be ‘witnessed’. And, a given state could still result from the superposition of two other states. More specifically, IF ‘left-handed’ or ‘right-handed’ are possible states of a photon, THEN a phenomenon which causes one photon to be witnessed, should also set the corresponding state belonging to its entangled counterpart.
An additional question that somebody could ask would be, ‘If I simply test the main component, with two matching, normal lasers (whose beams are not entangled), what would the result be?’ And I would guess, that the pulses should have equal amplitude, because if one pulse arrives circularly-polarized, then the other can just as easily arrive linearly-polarized, to the photo-detectors / photocells.
1: ) Actually, this arrangement would still not be enough to guarantee, that the light in both resulting beams is always polarized in the same (circular) direction. If the Transmitting Beam and the Signal Beam happened to be plane-polarized parallel to each other, and phase-shifted 90⁰, then the result would be, that the two resulting beams are polarized in opposite directions, assuming the asymmetric beam-splitter / combiner. In this case again, no useful transmission can take place. But for this reason, the difference between the results from the two photo-detectors can be used, resulting from the Receiving Beam, to detect the presence or absence of entanglement.
Transmission will only occur, in the case of the mentioned beam-splitter / combiner, when both the Signal and the Transmitting Beam are plane-polarized perpendicularly to each other, and 90⁰ out-of-phase. And so, this would be another phenomenon, which reduces the eventual, measurable amplitude of any effects.
What I am assuming is, that the amount of time over which the polarization of a laser’s beam stays the same, is also equivalent to its coherency-length, since polarization is really just the phase-position of one out of two plane-polarized wave-components with respect to the other. But, because the Signal Beam has been passed through a linear polarizer, the consistency of its polarization with that of the Transmitting Beam, could result from ecology – i.e., from the physical location of both the Transmitting apparatus and the Receiving apparatus.
There is a way to overcome this specific problem, but this solution will again, make the apparatus more complicated. After the Signal Beam has passed through a linear polarizer – for a result diagonal to the boundary in the beam-splitter / combiner – it can be made to pass through a material, which becomes birefringent when a voltage is applied. Under the correct conditions, such a voltage could quickly switch the angle of plane-polarization, of the Signal Beam, between two mutually-perpendicular directions, both diagonal to the beam-splitter / combiner. But the time this takes would me much longer, than the separation between the 2 pulses belonging to one set. So the laser, whose pulses are being phase-shifted and delayed, to result in the Carrier Beam, can be made to fire twice. And then the application could be made to work with 2 sets of 2 pulses from the Carrier Beam, instead of 1 set of 2. Made to work, assuming that any entanglement is possible to detect at all…
Care should be taken, not to do this with the Receiving Beam’s laser as well, that corresponds to the Signal Beam.