Bell's inequality

Definition

Bell's inequality is a mathematical expression that sets limits on the correlation of measurements made on two quantum systems that are entangled. It highlights the differences between classical and quantum physics by demonstrating that if local hidden variable theories were true, then certain statistical predictions would be constrained, which contrasts with the predictions of quantum mechanics. This concept plays a pivotal role in understanding quantum entanglement and the fundamental implications of Bell's theorem.

5 Must Know Facts For Your Next Test

1. Bell's inequality was first derived by physicist John Bell in 1964 and has since become a cornerstone in experiments testing the foundations of quantum mechanics.
2. Experiments testing Bell's inequality have consistently shown violations of the inequality, supporting the predictions of quantum mechanics and ruling out local hidden variable theories.
3. There are different forms of Bell's inequalities, including the Clauser-Horne-Shimony-Holt (CHSH) inequality, which is commonly used in experimental setups.
4. The violation of Bell's inequality implies that entangled particles exhibit correlations that cannot be explained by classical physics or any local deterministic theory.
5. Bell's inequality has significant implications for quantum information science, particularly in areas like quantum cryptography and quantum computing.

Review Questions

• How does Bell's inequality demonstrate the differences between classical and quantum physics?
  • Bell's inequality illustrates the contrast between classical and quantum physics by establishing limits on correlations predicted by local hidden variable theories. In classical physics, it is assumed that particles have predetermined properties that influence measurement outcomes. However, Bell's theorem shows that when measurements are made on entangled particles, the observed correlations can exceed these limits, indicating non-classical behavior consistent with quantum mechanics.
• Discuss the implications of violations of Bell's inequality in experimental settings.
  • Violations of Bell's inequality in experiments provide strong evidence against local hidden variable theories and support the predictions of quantum mechanics. When experiments are conducted with entangled particles, the correlations observed often exceed the classical limits set by Bell's inequality. This result not only confirms the non-local nature of entangled systems but also raises questions about the nature of reality and causality at a fundamental level.
• Evaluate how Bell's inequality and its violations contribute to advancements in quantum technologies such as quantum cryptography.
  • The understanding and experimental validation of Bell's inequality and its violations play a crucial role in advancing quantum technologies, especially in quantum cryptography. By demonstrating that information shared between entangled particles cannot be easily intercepted without detection, Bell's theorem provides a foundation for secure communication protocols. The inherent unpredictability and non-locality revealed through these violations ensure that any eavesdropping attempts would disturb the system, thereby alerting legitimate users to potential security breaches.

Related terms

Quantum entanglement: A phenomenon where two or more quantum particles become interconnected such that the state of one particle instantaneously influences the state of another, regardless of the distance separating them.

Local hidden variable theory: A theoretical framework suggesting that particles have predetermined properties (hidden variables) that determine their measurement outcomes, which would allow for classical explanations of quantum phenomena.

Bell's theorem: A fundamental result in quantum mechanics showing that no local hidden variable theory can reproduce all the predictions of quantum mechanics, thus highlighting the non-local nature of quantum entanglement.