## For Experiments with Entangled Photons, Establishing the violation of Bell Inequalities and pioneering Quantum Information Science - by The Nobel Committee for Physics 2022 - Article review

This document contains a review of the article: "For Experiments with Entangled Photons, Establishing the violation of Bell Inequalities and pioneering Quantum Information Science - by The Nobel Committee for Physics" by The Nobel Committee for Physics
To order to read the article select:https://www.nobelprize.org/uploads/2022/10/advanced-physicsprize2022.pdf
• The text in italics is copied from the article.
• Immediate followed by some comments

### 1. Entanglement and the Einstein, Podolsky and Rosen paradox - page 1

From the beginnings of quantum mechanics, the electrons in an atom were recognized to be entangled because of their mutual Coulomb interaction.
This type of entanglement should be called local-entangled.
The simplest case is the helium atom, which has two electrons.
Okay.
This first calculation was not, however, what prompted Schrödinger to call entanglement the characteristic trait of quantum mechanics. Rather, he was prompted by a paper published in 1935 by Albert Einstein, Boris Podolsky and Nathan Rosen (EPR).
Okay.
This seminal paper described the seemingly paradoxical consequences of entanglement between particles that are so distant that any interaction between them can be completely ignored.
How is this entanglement measured?

### Page 2

The basic notion in the EPR thought experiment is that distant members of an entangled pair are measured using operators that do not commute (see Figure 1).
This raises two important issues:
1. Physical processes can only be studied and explained by real experiments, not by thought experiments.
2. Mathematics can in principle, only be used to describe experiments or observations, actual performed. The result is that the mathematics (operators, functions) become much easier to understand.
In the original formulation, the position, x, and momentum, p, of moving particles satisfied [x, p] = ih.
Using real experiments it should be clear how the parameters x, p, i and h are 'measured' to satisfy this equation.

### Figure 1. A schematic of an EPR experiment

(1) Pairs of entangled particles are prepared in a singlet spin state and sent in opposite directions from a source S.
How do we know that these are entangled particles?
(2) The spin direction of each particle is, in this initial state, totally undetermined.
undetermined meaning: not known.
(3)At some distance from the source, one particle from each pair passes a measuring device operated by A, or Alice, that measures the spin component in the z-direction.
Okay
(4) After passing the measuring apparatus, the particle appears with quantized spin in the z-direction, with either spin up, or with spin down.
Okay.
(5) Due to the strict anti-correlation between the spin orientation of the particles in the pairs, at the same time as Alice’s particle appears with spin up in the z-direction, then B or Bob’s particle will appear with spin down in the z-direction.
What does this strict anti-correlation physical means? How do we know that this is true. This is the most difficult part.
(6) In this way, the measurement performed by Alice effectively acts as a measurement of the other particle even if no measuring device acts on this particle.
This type of reasoning is only possible under some 'very' strict conditions.
(7) The EPR paradox appears if Bob instead (of the z-direction) choses to measure in the x-direction.
There is nothing wrong in principle, if A measures a particle in z-direction and B in the x-direction.
(8) It then looks like there are sharp values for the spin in perpendicular directions, in clear contradiction to quantum mechanics
All what this experiment tells us is what the measurements show us. The same with quantum mechanics. So please inform the reader which are the experiments on which quantum mechanics is based.

### Page 3

Assume that a measurement by Alice gives =1/2. Then from Eq. (3) it follows that if Bob were to measure Sz also at B, we would get -1/2 with 100% probability; this is true event by event. But Bob can choose instead to measure Sx, and get a definite answer +1/2 or -1/2.
Science should start with performing many experiments. See: Reflection 1 - EPR experiment, 1.2 In two identical directions, 1000 times and 1.4 In two different directions, 1000 times
What these experiments show when entangled particles are used that when both particles are measured in the same direction there exists correlation.
when both particles are measured in different directions there is no correlation. The mathematical which discribes entanglement is when the direction of the spin for one particle is +x,+y and +z than the direction of the entangled particle is -x,-y and -z.
To use Eq.(3) instead has no sceintific meaning to predict the reality.
It thus seems that we can assign sharp values to both spin components.
Einstein, Podolsky and Rosen concluded: ‘From this follows that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality
It does not make much sense to discus the concept of a wave function, if it is not exactly known how this function is calculated based on observations.
The same with the meaning of: to commute.
In short the text is not very clear. Only what counts are the results of experiments.

### 2. Bell inequalities - page 3

Most working physicists, if they were interested in the issue, sided with Bohr, and especially so after John von Neumann presented a proof showing that it is impossible to complement quantum mechanics with ‘hidden variables’ that would determine the outcome of any experiment. Still, some people kept pondering problems related to the foundations and interpretation of quantum mechanics.
It is not necessary to introduce hidden variables to explain the EPR experiment.
For example, in 1957, Hugh Everett proposed the ‘many-worlds interpretation’ of quantum mechanics [5] as an alternative to the then-dominant ‘Copenhagen interpretation’. The latter comes in different variations, but the basic claim, following Bohr, is that there is a sharp distinction between the microscopic phenomena described by quantum mechanics and the macroscopic detectors used to study them, which are assumed to obey the laws of classical physics.
No physical process is supposed to obey the laws of classical machanics nor of quantum mechanics. If there is a conflict these laws should be adapted. At the same time we have to accepted the limitations of our measurements.
The many-worlds interpretation makes no such division, but instead purports that whenever a measurement takes place, a different world is created and that there is no connection between the different worlds.
Such a sentence requires a clear definition of what a measurement is. When I type this sentence I measure, and perform changes, continously. That each of these measurements, to find the keys to type, creates a different world, makes no sense.
In this interpretation, Schrödinger’s cat would be alive in one world and dead in another.
There exists only one world

### Page 4

Bell pointed out that von Neuman’s proof was not correct (he gave the proof of this statement in a later publication [8]), and he also formulated the first Bell inequality, which was a spectacular theoretical discovery.
Okay.
Using a special version of the Bohmian-EPR thought experiment, he showed mathematically that no hidden variable theory would be able to reproduce all the results of quantum mechanics.
It is doubtfull to perform science by using thought experiments. The experiment in "figure 1" is impossible to perform as a thought experiment.
Bell first derived an inequality for a certain correlation function that has to be obeyed by any local realist theory, and he then showed that for some experimental conditions the predictions of quantum mechanics violate this inequality.
More information is requiered to understand this sentence. Specific a definition of local realist theory.
The thought experiment considered by Bell is not suitable for experimental tests, simply because it makes assumptions about the detectors that cannot be justified for real equipment.
It does not make sense to discuss any process which cannot be created in reality. The problem could be that any physical measurement, disturbs the process to be measured.
The CHSH scenario shown in Figure 2 differs from the EPR thought experiment in that Alice can perform two different experiments that we denote by A1 and A2 (typically the measurement of the spin in two different directions, a1 and a2); similarly, Bob can measure B1 or B2.
Okay.
Assuming realism, the measurement outcomes one would obtain for each individual quantum system are well defined even if a measurement is not made.
For any process, specific for an experiment it is not necessary to perform actual measurements. The most important issue is that the experiment should be described carefully, such that each time the same results can be expected.
We then arrive at the inequality,
 < S > = |E(A1,B1) + E(A1, B2) + E(A2, B1) - E(A2, B2)| < 2 (5)
which holds for any realist theory.

### Figure 2. CHSH Scenario

(1) The source S produces pairs of entangled photons, sent in opposite directions
How do we know that these are entangled particles?
(2) Each photon encounters a two-channel polarizer whose orientation can be set by the Alice and Bob
Okay
We can now compare this result with what is predicted by quantum theory.
Quantum theory should predict the same as the experiments indicate.

### 3. The Freedman-Clauser experiment - page 5

The story might have stopped here. Some people said, 'Well, this is really weird', but dismissed that thought because the status quo already held that quantum mechanics is strange, Schrödinger’s cat is bizarre, and so on. And despite the bizarreness, it all seemed to work, so the inclination of the research community at the time was to just carry on using quantum mechanics to study new and exciting phenomena.
The results of experiments are never weird .
In the simplest case of the Schrödinger's cat experiment you place a cat alive in a box, you wait 5 minutes and you open the box. The cat is still alive.
After you place the cat in the box, what happens next is physics and has nothing to do, in principle, if the box is made from wood (1) or from glass (2).
In case (2) you can continously observe what happens with the cat and observe if the cat dies for what ever reason. You can also establish, by performing this experiment 1000 times, if the cat is ever both alive and dead.
In case (1) after closing the box, the state of the cat cannot be observed, but it does not make sense to claim that before opening the box that the cat is simultaneous alive and dead, while you know that physical (see case(2)), the cat can never be both alive and dead.
Thus, when he arrived at the University of California, Berkeley (UC Berkeley), to work as a postdoctoral researcher with Charles Townes in 1970, Clauser was prepared: he knew that Carl Kocher had built experimental equipment as part of his Ph.D. thesis at UC Berkeley in 1967 to study the time correlation between pairs of photons originating from a common source.
This is the same experiment as mentioned in 1.1 In two identical directions, once i.e. https://escholarship.org/uc/item/1kb7660q

### Page 5

Because the two photons have a common origin, they can be shown to be entangled.

### 1.1 In two identical directions, once

The idea behind an EPR experiment is to start with a reaction which creates 2 entangled particles (in opposite directions). For example: 2 electrons or 2 photons.
Typical reactions are collisions between a molecule and a proton or neutron which as a result creates these 2 entangled particles.
For an actual experiment to generate 2 entangled photons read this document:
https://escholarship.org/uc/item/1kb7660q
What this document actual shows is how important it is to perform real experiments and not thought experiments.

In this EPR experiment Alice performs the measurement in the z - direction and Bob also in the z - direction. The experiment is performed once.
The logic of this experiment is described in "Figure 1" line 5 and line 6 .
The outcome of this experiment is:

• when Alice measures a spin up in the z - direction, that Bob has 100% chance to measure a spin down in the z-direction.
• When Alice measures a spin down in the z - direction, that Bob has a 100% chance to measure a spin up in the z-direction

### 1.2 In two identical directions, 1000 times

The purpose of this specific is to establish a strict anti-correlation between the measurements of Alice and Bob. See "Figure 1"
line 1 and line 5

In reality it is not known before hand that such an experiment creates entangled particles. That means the same reaction has to be performed 1000 times, to establish that the 2 particles are correlated and what the correlation factor is. To quarantee that each experiment is performed identical and that the results should not influence each other, both paticles have to be measured in the same direction, simultaneous, a certain distance apart.
It is also important that 1/3 should be done in the x-direction, 1/3 in the y-direction and 1/3 in the z-direction.
The outcome of this experiment is

• There is a 50% chance that Alice measures a spin up in the z-direction, and when this is the case, there is a 100% chance that Bob measures a spin down in the z-direction
• There is a 50% chance that Alice measures a spin down in the z-direction, and when this is the case, there is a 100% chance that Bob measures a spin up in de z-direction
In short the outcome of Alice is unpredictable and when Alice knows, the outcome of Bob is predictable in the z-direction
What is important that this experiment has to be performed many times in order to establish that the particles are entangled.

This experiment is important because it shows that for any direction: When A measures +1, B will measure -1 and when A measures -1 B will measure +1.
For example when A measures +x, B will measure -x. When A measures -y B will measure +y and when A measures +z B measures -z. That means the results in each direction are strictly anti-correlated

The most important issue is that these results are not caused by these actual measurements, but are part of the original reaction.

### 1.3 In two different directions, once

In this EPR experiment Alice performs the measurement in the z - direction and Bob in the x - direction. The experiment is performed once
The logic of this experiment is described in "Figure 1"
line 7 and line 8 .
The outcome of this experiment is:
• when Alice measures a spin up in the z - direction there is a chance that Bob measures a spin up in the x-direction and a chance of a spin down in the x-direction.
• When Alice measures a spin down in the z - direction there is a chance that Bob measures a spin up in the x-direction and a chance of a spin down in the x- direction.
In short the outcome of both Alice and Bob are unpredictable.

### 1.4 In two different directions, 1000 times

In this EPR experiment Alice performs the measurement in the z - direction and Bob in the x - direction. The experiment is performed 1000 times
The logic of this experiment is described in "Figure 1"
line 7 and line 8 .
The outcome of this experiment is
• There is a 50% chance that Alice measures a spin up in the z-direction.
When this is the case, there is a 50% chance that Bob measures a spin up in the x-direction and a 50% chance a spin down in the x-direction
• There is a 50% chance that Alice measures a spin down in the z-direction. When this is the case, there is a 50% chance that Bob measures a spin up in the x-direction and a 50% chance a spin down in the x-direction
In short the outcome of both Alice and Bob are unpredictable, when two different directions are tested.
This means that it only makes sense to test the particles, 1000 times, both in the same direction to establish entanglement

The importance of this experiment is:

• When A measures x+ and B measures y- than the direction of the spin at A is: x+,y+ and the direction of the spin at B is: x-, y-. In this case the direction in the z axis is undefined.
• When A measures y+ and B measures z+ than the direction of the spin at A is: y+,z- and the direction of the spin at B is: y-, z+. In this case the direction in the x axis is undefined.

### Reflection 2 - EPR experiment - CHSH scenario.

The purpose of this experiment is to test two directions of two entangled photons simultaneous.
What that means if the direction of the spin at A is x+,y+ and z+ than the direction at B is x-,y- and z-.
• What this means is that when both Alice and Bob measure in the same direction i.e. the x-direction that when Alice measures x+ that Bob should measure an x- . This demonstrates that the two particles are entangled.
When the both measure in the y-direction that when Alice measures y- that Bob should measure an y+ . Again this demonstrates that the two particles are entangled.
This experiment should be performed 1000 times.
• What this means is that when both Alice and Bob measure in different directions i.e. Alice in the x-direction and Bob in the y-direction, that when Alice measures x+ and Bob measures y+, that the spin of the particle at Alice is x+y- and the spin of the particle at Bob is x-y+. The direction of the spin in the z-direction is unknown. The reasoning is because the particles are entangled.
When Alice measures in the x-direction and Bob in the z-direction, that when Alice measures x- and Bob measures z-, that the spin of the particle at Alice is x-z+ and the spin of the particle at Bob is x+z-. The direction of the spin in the y-direction is unknown. The reasoning is because the particles are entangled.

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Created: 11 Oktober 2020

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