## Blog

### Feb 2021: Discussion between Alex Khan and his brother (professor in physics) on Bell's Inequality:

**Question from brother:**

* *

*Since I was teaching quantum mechanics this semester, I am struggling to*

*understand Bell's inequalities and why hidden variables make a difference*

*in the experimental result. It is different if you just read about*

*something or if you try to teach it to students (which requires a more*

*thorough understanding). Are you aware of Bell's theory and do you have a*

*good reference?*

**Alex response part 1:**

I have been doing undergraduate and high school level quantum computing lectures as well. But very simplified. I did a lot of reading to understand Bell's Inequality:

My simple understanding and even more simplified for this email:

Einstein said that quantum mechanics was not a complete theory and would require hidden variables to explain phenomenon like entanglement. However, Dirac and others thought that entanglement didn't require any underlying hidden variables. It was much later that Bell devised a way to answer whether there were hidden variables or not.

I believe later the equation was modified by Clauser (and the three other scientists) to the CHSH inequality.

Bell's inequality was violated and thus it was shown that there are NO hidden variables and quantum mechanics is real (i,e. particles are in fact entangled and when one is measured, the other's state also immediately collapses, also that they were not already in the state when the entanglement happened)

The hidden variables would have somehow allowed a more complicated equation to somehow determine the behavior of the two entangled particles. However, as Bell's inequality shows, there is no need for such hidden variables.

However, people still challenged the proof saying there were various loopholes (locality, errors, free choice etc). Over time many other experiments were done to prove that there are no other properties in nature somehow influencing (eg, errors or something controlling the behavior of the two entangled particles) or communicating between two entangled particles.

I guess the proof is in the way probabilities work classically, and as observed with the behavior of two entangled photons. If one adds a filter to change the

Video to explain:

Part 1: https://www.youtube.com/watch?v=sAXxSKifgtU&t=0s

Part 2: https://www.youtube.com/watch?v=8UxYKN1q5sI&t=0s

Simple paper:

https://arxiv.org/pdf/2012.10238.pdf

Good explanation of Hidden Variables:

https://www.sciencedirect.com/topics/mathematics/bell-inequality

More on CHSH inequality:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.23.880

More complicated versions:

https://www.degruyter.com/document/doi/10.1515/phys-2017-0066/html

https://stanford.library.sydney.edu.au/archives/sum2012/entries/bell-theorem/

Paper on history of removing loopholes:

https://arxiv.org/pdf/2011.09296.pdf

A series of experiments were done to remove the free-will loophole (i.e. somehow the universe controls Alice and Bob, and we have no free will.)

https://arxiv.org/pdf/1805.04431.pdf

**Alex response part 2:**

This is a cute video from Jim Al Khalili that made the most sense conceptually. He goes into the whole topic of Bell's inequality. His equation might be wrong in the video.

https://youtu.be/ISdBAf-ysI0?t=1642 (start at 27:22)

The Secrets Of Quantum Physics with Jim Al-Khalili (Part 1/2) | Spark

Professor Jim Al-Khalili traces the story of arguably the most important, accurate and yet perplexing scientific theory ever: quantum physics.The story of qu...

youtu.be

This is a good explanation of the actual difference between the equation with hidden variables and the actual quantum results:

https://www.youtube.com/watch?v=f72whGQ31Wg

The EPR Paradox & Bell's inequality explained simply

Get MagellanTV here: https://try.magellantv.com/arvinash and get an exclusive offer for our viewers: an extended, month-long trial, FREE. MagellanTV has the largest and best collection of Science content anywhere, including Space, Physics, Technology, Nature, Mind and Body, and a growing collection of 4K. This new streaming service has 3000 ...

www.youtube.com

Ok finally here are five videos by Dr. Vazirani at Berkley. I saw one of his presentations when I went to a quantum computing conference in San Jose. He does the best job of giving context behind the whole hidden variables topic, and the paradox. Regarding entangled particles he says "nature can't be both local and follow global realism at the same time. Locality does hold, thus realism cannot...thus the state is really undetermined when you are not looking" (end of the last lecture below)

https://www.youtube.com/watch?v=Lu8cEBxupXY

Lecture 3 4 EPR PARADOX

www.youtube.com

https://www.youtube.com/watch?v=12aqJErA0vA

Lecture 4 1 BELL AND EPR

www.youtube.com

https://www.youtube.com/watch?v=ivmThsbkhTU

Lecture 4 2 ROTATIONAL INVARIANCE OF BELL STATE

Lecture 4 2 ROTATIONAL INVARIANCE OF BELL STATE

www.youtube.com

https://www.youtube.com/watch?v=sUQYSy6C1aA

Lecture 4 3 CHSH INEQUALITY

www.youtube.com

https://www.youtube.com/watch?v=8RYq-_1AfCM

Lecture 4 4 BELL AND LOCAL REALISM

Lecture 4 4 BELL AND LOCAL REALISM

www.youtube.com

**Response from my brother:**

*thanks for the many references to Bell's inequality. Watching all these*

*videos will probably keep me busy until I retire.*

*What you explained is of course right. My problem is that I can follow the*

*derivations in several textbooks line by line, but I am still unable to*

*say WHY it makes an experimentally observable difference whether two*

*particles know their spin beforehand or make up their mind only when a*

*measurement forces them to do so. There is a logical step which none of*

*these books bother to mention because maybe it is obvious - but not for*

*me. I think I am close, but not quite there.*

**Alex response part 3:**

It is like anything with quantum mechanics. lol. But I know exactly what you are saying. There are times I think I understand it, but then, I wonder if I do.

Ok let me try:

Similar to what Vazirani says in his last video (the last link in part 2) , I think, this text says it best:

***************

"2. What are the predictions made by local realism?

I think that this is really the crux of the problem, regardless of what the predictions made by quantum mechanics are. This is because Bell's Inequality does not state a prediction of QM -- it states a prediction of local realism (or of other sets of closely related philosophies, such as locality + counterfactual definiteness) -- and there is lots of evidence that the prediction of local realism made by Bells' Inequality does not hold. Thus, what QM predicts is only relevant if you are interested in one of its many interpretations to replace local realism. Of course, via these same experiments, the results tend to match the predictions of QM, so they also provide evidence for the QM equations, but I think that this not the main purpose of Bell's Inequality. Bell's Inequality is a very abstract statement designed to cover any local realism theory. So, since intuition is what we are after, allow me to propose a particular local realism theory, which the experiments for Bell's Inequality will therefore provide equally good evidence against"

*************

I got this from https://physics.stackexchange.com/questions/114218/bells-theorem-for-dummies-how-does-it-work

However,

the various videos and explanations show that with this "local realism" the probabilities should meet the inequality. The Probabilities can never be more than that. However, when we do experiments and observe how entangled particles behave it violates the inequality. The only way they "could" violate the inequality is something more than "local realism" is somehow happening. I think Vazirani calls this Global realism. Since we know how QM works, we can calculate this theoretically as well, and that violates Bell's inequality as well.

**Alex response part 4:**

One more thought.

Your two statements:

WHY it makes an experimentally observable difference whether

1) two particles know their spin beforehand or

2) make up their mind only when a measurement forces them to do so.

are both "classical". If I had a classical coin that was connected to another coin, and when I measure one, the other is the opposite, I think Bell's inequality would not be violated.

The situation, the way I see it, is this:

1) two particles know their spin beforehand (these are like two gloves, and are locally determined). The math for local determinism is Bell's inequality. It produces the straight line probabilities on the.

2) Quantum entanglement creates probabilistic answers which are NOT classical. This is only apparent when creating entangled particles and running them through polarizers. As you randomly rotate your polarizers the probabilities in certain regions violates ( i.e. moves above) the curve predicted by Bell's inequality. See the attached diagram. This is from one of the videos I sent. (See *Bell's inequality violation plot* image after this blog)

I think it is not that you are dealing with two boxes with coins that will flip. It is the quantum math and quantum observation when you measure the state with deferring basis angles. This calculation is fundamental to quantum computing, and how qubits probabilities are measured, however, they will violate classical expectation based on local realism. [and I will also add that the statement that the coin will "make up their mind when a measurement forces them to do so" is also classical and is not how entangle qubits behave when measured in the special apparatus]. I have seen that all ideas of classical measurement are violated with quantum measurements. eg. Stern-Gerlach experiment.

The more formal treatment is in the "simple paper" I attached in the first email on Bell's Inequality. 2012.10238.pdf (arxiv.org)

On page 10 it states, "BDM’s prediction exclusively concerns whether the local functions A(a, λ), B(b, λ), and hidden variables with probability distribution ρ(λ) can explain what has been experimentally found in four different series of actual experiments."

**Final response from my brother:**

* *

*thanks for the links. As for Bell's inequality, I followed the calculations*

*in several books, but I am still not convinced. Some logical step is*

*always missing.*

Important plot in this discussion:

Credit: Image: Bell's inequality violation plot.

This image is taken from the two part video https://www.youtube.com/watch?v=sAXxSKifgtU and https://www.youtube.com/watch?v=8UxYKN1q5sI

Also explained in https://www.youtube.com/watch?v=f72whGQ31Wg

-----end blog----------

### Aug 2020: Here is a high level preview of my Quantum Computing journey

We all have a unique journey into quantum computing. Some from physics, some from computer science, some from mathematics and others have taken a meandering path through the arts, education, engineering and corporate careers. My path is a combination of all of the above however, physics - curiosity of how the universe is made, how nature works and science was always in my blood. I took most things apart at home (except the car) much to my father's disappointment.

Below are some details of the key education and involvement that led to my initial skills, next courses and material that got me more specifically into quantum computing and finally the hands-on work and teaching that has helped me gain a deeper understanding of quantum computing. All this is tied up with a long career in IT from developing automation products to leading many million dollar projects and even bigger project portfolios.

It is a merging of a physics and engineering education, programming and product development career and entrepreneural interests.

College of Wooster Physics major Jr. Independent study in physics (research lab experiments on speed of light, e/m, gravitational constant G, Hall Effect, measuring resistance in superconducting material YBa2Cu3O7) mechanics, advanced math and modern physics courses

Purdue University Dual major physics/engineering, electricity and magnetism, quantum mechanics, advanced math, research paper on fourier transforms

Kansas State University major engineering (computational fluid mechanics, and combustion research)

Books and videos on Quantum physics and Cosmology by Greene, Guth, Fayer, Magueijo, Feynman and Hawking

MIT Open courses on Quantum Mechanics by Zwiebach

Interviews and books by Penrose

Quantum Mechanics lectures and many books by Suskind

D-Wave LEAP samples

MIT-xPro all 4 classes by Oliver, Chuang and Shor which included hands on exposure to IBM-Q

QML course by Wittek

Dabbling in Rigetti PyQuil

Preparing material for "Introduction to QC "class for Duke U.

Formulating a solution for Portfolio Optimization on IBM-Q using QAOA and D-Wave using QUBO at Chicago Quantum

Preparing material and teaching D-Wave, IBM-Q, Algorithms, Cryptography at Harrisburg U. Summer program

The most useful books to me have been Dancing with Qubits by Sutor, Programming Quantum Computers by Johnston, Harringan and Gimeno-Segovia and Quantum Programming Illustrated by Radovanovic

Reference books I use are Quantum Computing: An Applied Approach by Hidary, and Quantum Computation and Quantum Information by Nielsen and Chuang

In addition many jupyter notebooks and samples available in qiskit.org or textbook, and github samples

Qiskit videos by Asfaw

Reading over 50 research papers on Annealing, QAOA, VQE, quantum finance and other quantum computing topics

Attending many quantum presentations starting with the Washington DC meetup presentations by Chris Monroe (IonQ) and Michael Brett (then QxBranch, now Rigetti)

Attending many quantum conferences starting with Quantum Tech in Boston and Q2B in San Jose in 2019 but now online