Quantum Measurement Operator and Results: Exploring the Inverse Bell Theorem

In summary, there is a discrepancy between the predicted results of a separable measurement operator in quantum mechanics, which falls within the range of [-2;2], and the classical results, which would give a range of [-4;4]. This suggests that the process of going from a measurement operator to actual measurement results may be more complicated than simply retranscribing the terms. Additionally, while classical results cannot produce values for the CHSH inequality, this operator shows that there can be a difference between the eigenvalues and the actual measurement results. However, this is not always the case and the post is not entirely precise.
  • #1
jk22
729
24
if we consider a separable measurement operator $$(A+A')\otimes (B-B')$$ then quantum mechanics predict the result is in [-2;2]

Whereas going to classical results would give in [-4;4]

This could indicate that going from measurement operator in the quantum realm to measurement results is maybe more complicated than just retranscripting the terms ?
 
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  • #2
jk22, your post is not very coherent
jk22 said:
if we consider a separable measurement operator $$(A+A')\otimes (B-B')$$
Measurement operator represents measurements and in Bell test two measurement angles are always considered independent.
But measured pair of particles can be in separable or entangled state.

jk22 said:
then quantum mechanics predict the result is in [-2;2]

Whereas going to classical results would give in [-4;4]
Classical results can't give such values for CHSH inequality. Correlation values in inequality are not just arbitrary numbers but maximum numbers you can get when using shared initial variable for particle pair.
 
  • #3
Well this operator is not Chsh but it shows a discrepancy between eigenvalues and the measurement results since the value of each operator A,A',B,B' is in {-1;1} whereas if i consider the operators like in a bell test they cannot reach such eigenvalues but not in general this is true my post is not very precise.
 
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Related to Quantum Measurement Operator and Results: Exploring the Inverse Bell Theorem

1. What is the purpose of the Quantum Measurement Operator?

The Quantum Measurement Operator is used to describe the process of measuring a quantum system. It is a mathematical tool that helps us understand how the properties of a quantum system change when we observe it.

2. What is the Inverse Bell Theorem?

The Inverse Bell Theorem is a mathematical proof that shows the limitations of classical correlations in explaining the behavior of entangled quantum particles. It states that there is no local hidden variable theory that can reproduce all the predictions of quantum mechanics.

3. How does the Inverse Bell Theorem relate to the Quantum Measurement Operator?

The Inverse Bell Theorem is closely related to the Quantum Measurement Operator as it is used to demonstrate the non-locality and non-determinism of quantum mechanics. The theorem uses the results obtained from the measurement operator to show that classical correlations cannot fully explain the behavior of entangled quantum particles.

4. What are the implications of the Inverse Bell Theorem?

The Inverse Bell Theorem has significant implications for our understanding of the fundamental nature of reality. It suggests that there is a fundamental non-locality inherent in quantum systems, and that classical physical theories cannot fully explain quantum phenomena.

5. How does the Inverse Bell Theorem impact quantum technologies?

The Inverse Bell Theorem has a significant impact on the development of quantum technologies. It shows that the behavior of entangled quantum particles cannot be explained by classical theories and that there is a fundamental non-locality in quantum systems. This understanding is crucial for the development of technologies such as quantum computing and quantum cryptography.

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