Empirical verification of quantum entanglement 

The introduction of quantum entanglement gives an impression that quantum entanglement is empirically verified. A typical presentation goes like this.

An entangled pair of electrons moves away from each other. Alice measures the spin of one electron. It goes up. Bob measures the spin of another electron. It goes down. The measurement of the first electron by Alice instantaneously determines the spin of another electron for they are entangled.

The experiment must have been conducted many times. But the actual answer is never. The described experiment has never been conducted. I put a note from ChatGTP at the end of this note.

What have been performed are statistical results based on Bell’s inequality. There is a long chain of deductions between quantum entanglement and Bell’s inequality, with many explicit and implicit assumptions.  The discussion about quantum entanglement is far from settled.

A note from ChatGPT

Question: Why we can’t measure entanglement of individual pair of electrons?

Measuring the entanglement of individual pairs of electrons is a challenging task due to several reasons:

1. **Decoherence**: Entanglement is fragile and can easily be disrupted by interactions with the environment, a phenomenon known as decoherence. Measuring individual electron pairs typically requires isolating them from their surroundings to minimize decoherence, which is extremely difficult.

2. **Single-particle entanglement**: Entanglement typically arises in systems of multiple particles. While it is possible to prepare two electrons in an entangled state, measuring their entanglement directly without affecting their state is a significant technical challenge.

3. **Measurement problem**: Measuring the entanglement of a pair of particles usually requires performing measurements on each particle and then comparing the results. However, the process of measurement can change the quantum state of the particles, making it tricky to assess their initial entanglement accurately.

4. **No-cloning theorem**: The no-cloning theorem in quantum mechanics states that you cannot make an exact copy of an arbitrary unknown quantum state. This makes it difficult to directly measure the entanglement of individual pairs of electrons without altering their quantum states.

In practice, scientists often use statistical methods and ensembles of particles to study entanglement because it's easier to manipulate and measure large quantities of particles. While progress has been made in single-particle entanglement studies, it remains a complex and challenging area of research due to the fundamental principles of quantum mechanics.