Comments about "Quantum entanglement" in Wikipedia

This document contains comments about the article "Quantum entanglement" in Wikipedia

• The text in italics is copied from that URL
  
• Immediate followed by some comments
  

In the last paragraph I explain my own opinion.

Contents

• 1. History
• 2. Concept
• 2.1 Meaning of entanglement
• 2.2 Paradox
• 2.3 Hidden variables theory
• 2.4 Violations of Bell's inequality
• 2.5 Notable experimental results proving quantum entanglement - 2024
• 2.6 Emergence of time from quantum entanglement - 2024
• 2.7 Emergent gravity - 2024
• 3. Non-locality and entanglement
• 4. Quantum mechanical framework
• 4.1 Pure states
• 4.2 Ensembles
• 4.3 Reduced density matrices
• 4.4 Two applications that use them
• 4.5 Entanglement as a resource
• 4.6 Classification of entanglement
• 4.7 Entropy
• 4.7.1 Definition
• 4.7.2 As a measure of entanglement
• 4.8 Entanglement measures
• 4.9 Quantum field theory
• 5 Applications
• 5.1 Entangled states
• 5.2 Methods of creating entanglement
• 5.3 Testing a system for entanglement
• 6. Naturally entangled systems
• 7. Entanglement of top quarks
• 8. Entanglement of macroscopic objects
• 8.1 Entanglement of elements of living systems
• 9. See also

Reflection

• Reflection 1 - Measurement
• Reflection 2 - Testing correlation
• Reflection 3 - Quantum Entanglement Paradox - 22 May 2018
• Reflection 4 - Quantum Conformance Test - 19 Jan 2022
• Reflection 5 - Polarization Correlation of Photons Emitted in an Atomic Cascade - by Carl Alvin Kocher 1967

Introduction

General note: To understand and evaluate the document is difficult because the difference between correlated and entangled is not explained.
The article starts with the following sentence.

Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently of the others, even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.

This sentence is not clear. Part of the problem is that what is meant with quantum state of a particle and most of all with the quantum state as a whole.
. It should be mentioned that in almost all systems consisting of objects which influence each other by means of forces it is almost impossible to establish the state of each object simultaneous. Simulataneous meaning at the same instant in time. State meaning the position and velocity in 3D. See also: conflict

Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated.

It should be mentioned that the meaning of the word entangled is not explained. It should be mentioned that to measure the momentum of any object (which involves the measurement of mass and v) requires many measurements. To make all this easier to understand, the concept: "in some cases", should be better explained.

For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise.

IMO the only way to create two particles in a closed system with the possibilty that the total spin is zero is that when one particle rotates clockwise and the other particle counterclockwise
With a closed system is meant that the two particles influence each other by means of forces.
The question is how is the spin of one particle measured. When the spin of one particle is measured and disturbed then the second particle is also disturbed. This makes it impossible to measure the original spin of the second particle and as such the total spin.

However, this behavior gives rise to seemingly paradoxical effects: any measurement of a particle's properties results in an apparent and irreversible wave function collapse of that particle and changes the original quantum state.

This sentence demonstrates one important problem: In one sentence you should not use both concepts: particles and wave function.
There exist no paradox: any measurement of a particle in a closed system influences the state (position) of that particle which in turn influences the state (positions) of all the other particles. That is the physical reality. A closed system in this case is an atom.
This situation is more or less also discussed at the section at the beginning of this document: https://en.wikipedia.org/wiki/Spin_(physics)#Compatibility_of_spin_measurements See:

This means that if, for example, we know the spin along the x axis, and we then measure the spin along the y axis, we have invalidated our previous knowledge of the x axis spin.

My interpretation is when the spin of the x axis is measured and is available. Then when thereafter the spin of the y axis is measured, that during this process the spin the x-axis is disturbed and again becomes unknown.

With entangled particles, such measurements affect the entangled system as a whole.

The problem with this document is that neither the concept entangled particles or entangled system is clearly defined.
A simpler sentence is: With electrons, any measurement affects the atom as a whole.

Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrödinger shortly thereafter, describing what came to be known as the EPR paradox. Einstein and others considered such behavior impossible, as it violated the local realism view of causality (Einstein referring to it as "spooky action at a distance") and argued that the accepted formulation of quantum mechanics must therefore be incomplete.

These sentences are not very clear.
See: Reflection 5 - Polarization Correlation of Photons Emitted in an Atomic Cascade - by Carl Alvin Kocher 1967
In this document Carl Kocher describes an experiment which generates two photons, with each a particular frequency, originating almost simultaneously from a common source. That means when the frequency of each photon later is measured only 2 answers are possible. The logical conclusion is that the result of each measurement shows, both, the result when measured but also at the instant of creation. A different conclusion is that both frequencies should not be the same.
Any way no "spooky action at a distance" is involved. All the action is locally and part of the original reaction.

1. History

In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper on the counterintuitive predictions that quantum mechanics makes for pairs of objects prepared together in a particular way.

May be all what is written is correct, but in total it is not clear.

In this study, the three formulated the Einstein–Podolsky–Rosen paradox (EPR paradox), a thought experiment that attempted to show that "the quantum-mechanical description of physical reality given by wave functions is not complete."

May be all what is written is correct, but in total it is not clear. The question is to what extend a thought experiment can be used in the realm of quantum mechanics.

However, the three scientists did not coin the word entanglement, nor did they generalize the special properties of the quantum state they considered.

IMO this section has to be rewritten.

An early experimental breakthrough was due to Carl Kocher, who already in 1967 presented an apparatus in which two photons successively emitted from a calcium atom were shown to be entangled – the first case of entangled visible light.

In his time Carl Kocher called this "Polarization Correlation of Photons", which is the correct name.
His experiments demonstrates that the two photons are created from a common point, inside the reaction, more or less instantaneous.
He did not mention that there is any physical link between the two photons.
For more detail see: Reflection 5 - Polarization Correlation of Photons Emitted in an Atomic Cascade - by Carl Alvin Kocher 1967

2 Concept

2.1 Meaning of entanglement

An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole.

This sentence is not clear. It is important to start with an experiment which creates entangled particles.

In entanglement, one constituent cannot be fully described without considering the other(s).

This sentence is not clear. It is important to start with an experiment which creates entangled particles.

The state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum cannot be written as a single product term.

This sentence is not clear. It is important to start with an experiment which creates entangled particles.

Quantum systems can become entangled through various types of interactions.

I expect interactions between Qubits. This is the case when the operation of a Quantum Computer is discussed.

Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.

Decoherence is typical the case when Qubits are considered, because Qubits are not considered as stable.
In a Quantum Computer the operation of the Quantum system stops when a measurement is made to demonstrate the final result. This is typical the case in the Shor Algorithm. In that case at the end of the execution of the Algorithm a measurement should be made in order to stop the execution. There after the final answer will be displayed.

conflict

As an example of entanglement: a subatomic particle decays into an entangled pair of other particles. .

This makes only sense if entanglement is considered a normal condition of all elementary particles.

The decay events obey the various conservation laws, and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process).

Okay

For instance, a spin-zero particle could decay into a pair of spin-½ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be spin up on some axis, the other, when measured on the same axis, is always found to be spin down.

Okay

The above result may or may not be perceived as surprising.

2.2 Paradox

The paradox is that a measurement made on either of the particles apparently collapses the state of the entire entangled system – and does so instantaneously, before any information about the measurement result could have been communicated to the other particle and hence assured the "proper" outcome of the measurement of the other part of the entangled pair.

More detail is required. I expect that the same problem arises if you want to calculate the speed of a particle.

In the quantum formalism, the result of a spin measurement on one of the particles is a collapse into a state in which each particle has a definite spin (either up or down) along the axis of measurement.

More detail is required what is meant

The outcome is taken to be random, with each possibility having a probability of 50%.

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However, if both spins are measured along the same axis, they are found to be anti-correlated. This means that the random outcome of the measurement made on one particle seems to have been transmitted to the other, so that it can make the "right choice" when it too is measured.

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The distance and timing of the measurements can be chosen so as to make the interval between the two measurements spacelike, hence, a message connecting the events would have to travel faster than light.

The two particles are correlated. To demonstrate that does require two measurements, but these measurements itself do not require any communication. The cause is in the original reaction when the two particles where created.

According to the principles of special relativity, it is not possible for any information to travel between two such measuring events.

It is not even possible to unambiguously say which of the measurements came first.

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Therefore, the correlation between the two measurements cannot appropriately be explained as one measurement determining the other.

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Different observers would disagree about the role of cause and effect.

All what is written above is not very clear. What is important that general speaking in any physical process, observers are not part of the process. Observations or measurements can be made, but they are not important for the evolution of the process, which should evolve indepent if measurements are made or not.
All measurements or observations are considered as events. The time of these events should be properly monitored, such they can later be evaluated.

2.3 Hidden variables theory

A possible resolution to the paradox might be to assume that the state of the particles contains some hidden variables, whose values effectively determine, right from the moment of separation, what the outcomes of the spin measurements are going to be.

Not clear.

2.4 Violations of Bell's inequality