Quantum Entanglement #

Quantum entanglement is a fascinating phenomenon where two or more particles become correlated in such a way that the quantum state of each particle cannot be described independently, even when separated by large distances.

Mathematical Description #

The simplest example of an entangled state is the Bell state, also known as an EPR pair. For two qubits, one of the Bell states can be written as:

This state cannot be written as a product of individual qubit states, which is a key characteristic of entanglement.

Physical Interpretation #

When we measure one particle of an entangled pair:

• The state of the other particle is instantly determined
• This happens regardless of the distance between particles
• The measurement results are correlated, but we cannot use this for faster-than-light communication

Famous Example: EPR Paradox #

Einstein, Podolsky, and Rosen (EPR) used entanglement to challenge quantum mechanics, suggesting it was incomplete. Consider two entangled particles in the state:

This is a “singlet state” where the spins of the particles are always opposite, demonstrating the “spooky action at a distance” that Einstein found troubling.