EPR paradox and spooky action

Quantum Entanglement

Explore the mysterious quantum phenomenon Einstein called "spooky action at a distance"

What is Quantum Entanglement?

Quantum entanglement is a phenomenon where two or more qubits become correlated in such a way that the measurement of one instantly determines the state of the others, regardless of the distance between them.

Key Properties:
  • Non-locality: Instantaneous correlation across any distance
  • Measurement correlation: Measuring one affects the other
  • No communication: Cannot transmit information faster than light
  • Fragility: Easily destroyed by environmental interference

Bell States

Bell states are the four maximally entangled two-qubit states that form the basis for many quantum protocols.

Interactive Bell State Demo
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Current Bell State: |Φ⁺⟩ = (|00⟩ + |11⟩)/√2

Bell's Inequality

Bell's inequality provides a way to test whether quantum mechanics violates local realism. Quantum systems can violate this inequality, proving non-locality.

Bell Inequality Test

Classical physics: |E(a,b) - E(a,c)| + |E(b,c) + E(b,d)| ≤ 2

Quantum mechanics can achieve: 2√2 ≈ 2.828

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EPR Paradox

The Einstein-Podolsky-Rosen paradox questioned the completeness of quantum mechanics, leading to the development of Bell's theorem.

Alice and bOb Experiment
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Alice
Angle: 0°
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Entangled Pair

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bOb
Angle: 0°
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Correlation: -

Expected: cos²(θ) where θ is angle difference

Quantum Teleportation

Quantum teleportation uses entanglement to transfer quantum states from one location to another without physically moving the particle.

Teleportation Protocol
1. Prepare
Entangled pair + unknown state
2. Bell Measurement
Joint measurement
3. Classical Communication
Send measurement result
4. Reconstruction
Apply correction operation

Bell States

  • |Φ⁺⟩: (|00⟩ + |11⟩)/√2
  • |Φ⁻⟩: (|00⟩ - |11⟩)/√2
  • |Ψ⁺⟩: (|01⟩ + |10⟩)/√2
  • |Ψ⁻⟩: (|01⟩ - |10⟩)/√2

Applications

  • Quantum Cryptography
  • Quantum Teleportation
  • Quantum Computing
  • Quantum Sensing
  • Quantum Networks

Key Concepts

  • Non-locality: Instant correlations
  • Bell's Theorem: No local hidden variables
  • Measurement: Collapses entanglement
  • Decoherence: Environmental destruction

Next Topics

Quantum Cryptography Quantum Gates Quantum Algorithms