Thursday, October 6, 2022

Three Physicists Share Nobel For Bold "Nonlocality" Experiments That Paved The Path to Quantum Computing


Einstein's take on quantum mechanics "God does not play dice".

The announcement of the Nobel Prize in Physics to three pioneering quantum physicists(Alain Aspect, John F. Clauser and Anton Zeilinger ) is - I believe - one of the more noteworthy awards in the past six decades. Perhaps on the level of  the discovery of the 3K cosmic background radiation by Penzias and Wilson, which established the validity of the Big Bang. The 10 million Swedish kronor award, equivalent to $918,000, will be split evenly between Dr. Aspect of the Université Paris-Saclay and École Polytechnique in France, Dr. Clauser, whose research was done when he was at Columbia University, and Dr. Zeilinger of the University of Vienna in Austria.

According to most media reports (.e.g in the WSJ, NY Times etc.) the  trio’s work was cited by the Nobel committee as having laid the foundation for a “new era of quantum technology, enabling the construction of quantum computers and networks."  In fact, their work was at a much more foundational and pure physics research level.  It is that background work I want to elaborate in this post.

Dr. Clauser, in an interview Tuesday with the Associated Press, said that his work on quantum mechanics shows that you "can’t confine information to a closed volume, say like a little box that sits on your desk.”   But this very feature, which Einstein considered "spooky action at a distance" is why the revered physicist opposed quantum mechanics.

This is what I want to explore further , by first noting first that Clauser built his work on Bell’s theorem.  

In a landmark theoretical achievement in 1964, mathematician John S. Bell formulated a thought experiment based on a design similar to that shown in the crude sketch below in which electrons of differing spin fly off to two separate detectors  d1 and  d2:

d1 (+ ½ )<--*---[ o  ]----*-->(- ½ ) d2  

 Einstein, Podolsky and Rosen (E-P-R) .[1] originally  imagined a quantum system (atom= o) which could be 'ruptured' such that two electrons (*) were dispatched to two differing measurement devices. Each electron would carry a property called 'spin'. Since the atom had zero spin, this meant one would have spin (+ 1/2), the other (-1/2).

Orthodox quantum mechanics forbade the simultaneous measurement of a property (say different spin states) for the same system. If you got one, you could not obtain the other. This was a direct outcome of the Heisenberg Indeterminacy Principle which stated that simultaneous quantum measurements could not be made to the same precision.

E-P-R argued that this showed the incompleteness of quantum mechanics. It was not the 'paragon' of physical theories its apologists claimed, especially if such indeterminacy was fundamentally embedded within it.  

But years later, in 1964 (as I noted) mathematician John S. Bell asked the question: 'What if the E-P-R experiment could actually be carried out? What sort of mathematical results would be achieved?

In a work referred to as "the most profound discovery in the history of science", Bell then proceeded to place the E-P-R experiment in a rigorous and quantifiable context, which could be checked by actual measurements.

Bell made the basic assumption of locality (i.e. that no communication could occur between  the detector  d1 and detector  d2 at any rate faster than light speed). In what is now widely recognized as a seminal work of mathematical physics, he set out to show that a theory which upheld locality could reproduce the predictions of quantum mechanics. His result predicted that the above sum, S, had to be less than or equal to 2 (S less than or equal 2). This became known as the 'Bell Inequality'.

The original form of the experiment invoked the quantum state of a two particle system in which position differential (x1 - x2) and momentum sum (p1 + p2)are both determined. Then the wave function is:

y (x1, x2) = f(x1 - x2 -a) =   å  ¥ k=0  c k exp[ik(x1 - x2 -a)]

where the summation is over the k elements; f(x1 - x2 -a) is a packlet function sharply peaked at (x1 - x2) = a.  
Alternatively, if p is measured, then one knows immediately that p2 = -p1 since p1 + p2 = 0. In both cases the 1st particle is "disturbed" by measurement and this accounts for the Heisenberg uncertainty relations applied in 1-d. However, the 2nd particle is taken not to interact with the 1st at all- so one can obtain its properties minus the assumption of any disturbance.

The first highly refined experiments to test quantum conformity to Bell's Theorem were performed by Alain Aspect and his colleagues at the University of Paris.[2] In these experiments, the detection of the polarizations of photons was the key. These were observed with the photons emanating from a Krypton-Dye laser and arriving at two different analyzers A1 and A2, e.g.

Here, the laser device is D, and the analyzers (polarization detectors) are A1 and A2 along with two representative polarizations given at each, for two photons P1 and P2. The results of these remarkable experiments disclosed apparent and instantaneous connections between the photons at A1 and A2. In the case shown, a photon (P1) in the minimum (0) intensity polarization mode, is anti-correlated with one in the maximum intensity (1) mode.

To fix ideas and show differences, in the Aspect experiment four (not two - as shown) different analyzer orientation 'sets' were obtained. These might be denoted: (A1,A2)I, (A1,A2)II, (A1,A2,)III, and (A1,A2)IV. Each result is expressed as a mathematical (statistical) quantity known as a 'correlation coefficient'.   One then obtained, for example:  

S = (A1,A2)I + (A1,A2)II + (A1,A2,)III + (A1,A2)IV

Remember that for locality to be preserved (in line with the E-P-R experiment), Bell showed that one required:  S  <  2.  However, Aspects; experiments showed:

S =  2.70 ± 0.05  

In addition, Aspect's experiment closed an important loophole in Dr. Clauser's work by proving that 'hidden variables' theories couldn't replace quantum mechanics. So Dr. Aspect killed 'two birds' with once stone: showing quantum mechanics is not incomplete, as EPR claimed, and further than there was no need to revise it using a Heisenberg relation with hidden variables.

This also marked the first ever hint of "entanglement" which would subsequently become a primary basis for quantum computing.  Hence, Aspect, Clauser and Zeilinger did not 'discover" quantum computing - as one may be led to believe from superficial media accounts - but they did the foundational quantum experiments that have led to its further technological development. (Zeilinger himself is credited with experiments to do with "quantum teleportation", whereby a quantum state is transferred from one particle to another at a distance.)

One last bold effort was made to salvage hidden variables in a paper by Rietdijk and Selleri, appearing in Foundations of Physics, in 1983:

But even they were forced to admit (p. 312):  

"One can escape the foregoing argument, deriving nonlocality from quantum mechanics, only by giving up the experimenter's free choice, i.e. by assuming superdeterminism."  

By that they meant the two detectors at A1, A2 would only be able to obtain measurements as prescribed by quantum mechanics provided the decisions for determination (say of the polarizations of the photons) were "pre-coordinated".   One would then obtain "nonlocal pre-coordination" between mutually distant measurement events.  The authors concede this is "far more beyond current conceptions than a simple nonlocal influence", but also argued it could not be "absolutely excluded".   

Well, ok, but in the same vein the sudden migration of all the air molecules in the room I'm in - say to one corner- suffocating me, cannot also be "absolutely excluded" from happening.  But I am not terribly worried that it will.  

The mighty success of the Aspect/Clauser experiments as well as Zeilinger's quantum teleportation proposal has been more than amply demonstrated with the kind of secure communications used in China's Micius satellite (see link to a previous post I wrote, below).

In ending it is important to bear in mind just how violently opposed Einstein was to the whole notion of quantum mechanics, especially the uncertainty or indeterminacy principle.  This is what elicited his famous "God does not play dice with the universe" quote and which initiated a debate with Neils Bohr that went on for some time, even before the E-P-R experiment.  To get an idea of the lengths Einstein went to, in order to prove Bohr (and quantum mechanics) wrong, it is instructive to check out this earlier post below- which includes the ingenious device Einstein conceived to try to trip up Bohr.  It is well worth a read again, especially that section to do with Einstein's thought experiment:

See Also;

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