A misconception that can exist, in Quantum Mechanics.

First of all, I need to admit that I did not study Quantum Mechanics. I did study Physics, however, and have had numerous discussions with people, who either:

  • Studied Quantum Mechanics independently, Or
  • Studied Quantum Mechanics formally.

And those discussions have made me aware of a misconception that can exist, about how the wave-function of particles lead to measurement, but which will certainly not exist, for people who have studied the subject formally.

I have already made a posting, about The Myth Of Wave-Particle Duality, in which I highlighted what I see as an absurdity, in how the wave-function of particles is commonly defined. And, having written that, I should also point out, that the common sense which QM applies, not to treat Complex Eigenvalues as representing real properties of a particle, fails to spill over, to Complex Probabilities.

Even though the wave function of certain particles can be taken to exist factually, attempts to measure it as belonging to one particle will cause it to collapse. However, the way some people may visualize it, would be, that the wave-function continues to exist, simply because the Universe seems to be filled with waves, that continue to exist. And this is an especially possible misinterpretation of QM when the particle in question is a photon, just because low-energy photons, that lead to long and obvious wavelengths – i.e., radio waves and light from lasers – are so commonplace.

What happens with these obvious waves is that, most of the time, a large number of photons contribute to those waves, in such a way that each photon is being absorbed, in order for the actual wave to have been measured. And, when the photon is absorbed, as I have written elsewhere, it has also been ‘witnessed’, so that it is no longer in a superposed state. And, because one photon has been absorbed, it has also ceased to exist.

Even the way photons ‘work’ changes drastically, when individual photons have been measured. Modern physics is capable of measuring individual photons. When this happens, the detection of one photon either took place or did not. This can also loosely be described as ‘a click’, in contrast with ‘a wavelike phenomenon’, even if a more sophisticated method has been used, than methods that produce audible clicks. And it continues to be true for the low-energy photons, of which there will typically be a greater number, as it was with high-energy photons, that Historical Technologies such as a Geiger Counter were able to detect. This digital existence of single photons, when measured as such, is universal.

I suppose that a valid question which the reader may next ask could be, ‘How would this apply to Quantum Computing, which factually performs computations, based on wave-functions?’ And, there are basically two types of answers which I can think of. The actual Quantum Computer is a tiny device, that can work with individual photons, But:

  • When Scientists measure the output of a Quantum Computer, they may be using a larger number of actual Quantum Computers, all performing exactly the same computation, but in such a way that the combined light intensity is high enough to be measured directly at any instant in time, Or
  • They may be amplifying the photon which one Quantum Computing core actually outputs, so that one output photon leads to a more macroscopic phenomenon, through which Scientists can read the result of a Quantum Computation, Or
  • The optics of a single Quantum Computing core can cause numerous photons to perform the same computation.

Either way, even though the state within the Quantum Computer was defined in terms of QBits, what gets measured as output, is no longer so. Therefore, the Quantum Algorithm needs to be programmed in such a way, that the ability either to measure a photon or not to, will still lead to a successful experiment.

What I do know additionally is, that if the photon output by a Quantum Computer has been amplified, let’s say by a laser-like device, any superposition of the wave-function of the original photon has been collapsed, because, when lasers are used as light amplifiers, they also witness the Quantum State of the initial photon. (:1) At that point, the Quantum Computation has definitely ended.


 

 

One of the more remarkable observations I seem to have made about QM is, that ordinary refraction or reflection of light, such as by metallic surfaces or glass, does not seem to witness the photons. Anecdotally, the reader may present himself to his washroom mirror in the morning, secure in the knowledge that the mirror did not witness what the reader sees.  ;-) This form of light can continue in some superposed state. The reason I’ve concluded this, is the large number of experiments which Scientists carry out, and then write about, and which still seem to succeed, in spite of the fact that the Scientist’s apparatus has refracted or reflected the light used.

Now, whether the Scientist actually noticed, that he was refracting or reflecting the light, is a separate question. I suppose that if the experiment failed, the next thing the Scientist will naturally do, is search for why…

(Updated 7/12/2020, 14h55… )

(As of 7/11/2020: )

1:)

This is a proposition, which ‘true believers’ tend to word differently, from how I worded it here. It sets up, what Quantum Mechanics refers to as its “No-Cloning Theorem”.

According to the formal definition, there could be two systems of quantum states, that describe the photon. In one system, the base-vectors define moments of circular polarization, while in another system, they define moments of linear polarization. What will happen is, that either system of quantum-states can be derived from the other, as a linear combination of the other’s states, with complex numbers as multipliers. This derivation of one system of states from the other, is in fact a superposition of the states, that one photon’s state derives from.

According to the no-cloning theorem, a laser will be able to clone states according to one system, but not states according to the other. Hence, A laser could possibly clone the linear polarization of a photon. But, as soon as this is possible, the laser will not be able to clone the photon’s state of circular polarization, because it only exists as a superposition of linearly polarized states.


 

 

(Update 7/12/2020, 7h00… )

Call me superstitious, but what I frequently slip into concluding is, that the photon’s state of ‘linear’ polarization is ultimately more real, and not just a superposition of its state of ‘circular’ polarization. However, since an experiment which I once conducted – using very basic apparatus – revealed, that the state of polarization of a beam of light can just be converted back and forth between linear and circular as many times as desired (consistently with what would be possible, purely according to the wave-based explanation of light), I need to state my own description as being the lesser, that if a beam is made ‘linearly polarized’ with a probability of 100%, its superposed state between two circularly polarized states be ~collapsed~. The beam can then be made circularly polarized again, without considerable loss to the total number of photons. Therefore, instead of the state of superposition really being collapsed, it has simply been ‘witnessed as one state’.


 

The No Cloning Theorem has a very practical implication, for the (im)possibility of what is sometimes referred to as ‘Counterfactual Communication’. Scientists have determined in numerous experiments, that a single source (beam) of light can be passed through certain crystals, which split it into two beams, the photon energy of each becoming half that of the original beam. And, importantly, the photons in one beam will be entangled with the photons in the other. In some popular accounts, this gets referred to as ‘spooky interaction at a distance’.

Because the photons are entangled, certain manipulations performed on one photon, affect the corresponding property of the other (Even when there is no direct link between the devices acting on the two beams!) Specifically, superposed states are used, and when the state is witnessed in one beam, the corresponding state in the other beam has also become non-random, instead being equal or opposite, whichever the case may be, to what the state was witnessed as, in the transmitting beam. (:2)

There is really no way to confirm that the photons in two beams are entangled, without there being any communication at all between the two beams. Therefore, what some researchers have looked for, is a way to harness entanglement, for some practical concept of communication. And researchers run into a basic barrier:

As one of the beams becomes attenuated, the strength of the link also becomes attenuated. Apparently, attempts to amplify one beam or both beams, fail to keep their states superposed, and as soon as their states are no longer so, counterfactual communication stops. Counterfactual communication ‘works’, until one of the beams reaches a laser-like device, that’s intended to amplify it.

However, it seems that passing one of the beams through a length of optical fibre does not stop entanglement of its particles, with the particles in the other beam, in a way that can still be measured.

What this means for practical communication is that:

  • The transmitting beam must be highly focussed, meaning that many of its photons reach the intended transmitter, so that the modulations that reach the intended receiver are strong enough to be measured reliably, And
  • The receiving beam must also be highly focussed, since the relationship is bidirectional. Photons scattered from the intended receiving beam, would turn it into a transmitting beam, and compromise the ability of the intended transmitting beam to modulate its no-longer-superposed states, Or
  • Counterfactual communication is doomed to fail.

And, even if the original beam did have many photons, the degree with which the would-be receiver can measure modulation, depends on what percentage of the photons starting out in the transmitting beam, reach the transmitter, Not, how many photons reach the transmitter…


 

 

(Update 7/12/2020, 14h55: )

2:)

I think that the way the problems of entanglement are sometimes stated, to be short, can lead to ambiguity. What a person may say is, that ‘The superposition is collapsed, when the photon has been witnessed, either from the transmitting beam, or from the receiving beam,’ but then, what some people may not define is, ‘which state of superposition':

  1. The superposition between the states, that are to be communicated between the entangled beams, Or
  2. The superposition between circularly polarized states, leading to a linearly polarized state, at one end of the apparatus, Or
  3. The superposition between linearly polarized states, leading to a circularly polarized state, at one end of the apparatus, If the counterfactual communication is to take place, using circular polarization.

If the context is counterfactual communication, it would seem to follow that superposition (1) has been collapsed, not (2) or (3).

Dirk

 

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