Quantum Entanglement: Spooky Action at a Distance
Explore how two particles can share quantum states regardless of the distance separating them.
Introduction
Quantum entanglement is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the quantum state of each particle cannot be described independently of the others, even when separated by large distances.
Mathematical Description
For a two-qubit system, an entangled state (Bell state) is written as:
|Φ⁺⟩ = (1/√2)(|00⟩ + |11⟩)
This state cannot be factored into a product of individual qubit states, which is the defining characteristic of entanglement.
EPR Paradox
In 1935, Einstein, Podolsky, and Rosen (EPR) published a thought experiment challenging quantum mechanics. They argued that if quantum mechanics were complete, it would violate the principle of local realism.
Bell's Theorem
John Bell (1964) devised a mathematical inequality (Bell inequalities) that, if violated, would rule out local hidden variable theories. Experiments by Aspect et al. (1982) conclusively demonstrated these violations.
Applications
- Quantum Cryptography: Quantum key distribution (QKD) using entangled photons
- Quantum Teleportation: Transfer of quantum states using entanglement + classical communication
- Quantum Computing: Entanglement as a computational resource for quantum speedup
See Also
- Bell States
- Quantum Teleportation
- Quantum Key Distribution