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Quantum Entanglement

Quantum entanglement is a correlation between quantum particles where the quantum state of the system cannot be described as a product of individual particle states, creating non-classical correlations that persist regardless of distance.

What it means

Entanglement occurs when two or more qubits become correlated in such a way that the quantum state of the system cannot be factored into individual qubit states.An entangled state like (|00⟩+|11⟩)/sqrt(2) means measuring one qubit as |0⟩ instantly implies the other is |0⟩ too.Einstein called this 'spooky action at a distance,' but Bell's theorem (1964) proved these correlations are genuinely quantum and cannot be explained by local hidden variables.Entanglement is not just a curiosity -- it is the key resource enabling quantum computing speedups, quantum teleportation, quantum cryptography, and quantum error correction.Entanglement can be quantified by measures such as entanglement entropy and concurrence.

Everyday analogy

Entanglement is like a pair of gloves shipped in separate boxes -- opening one and finding a left glove instantly tells you the other is right, but in quantum mechanics, the 'handedness' doesn't exist until you look.
Think of entangled particles as quantum dance partners -- no matter how far apart, they always perform perfectly complementary moves.

Common misconceptions

  • Entanglement does NOT allow faster-than-light communication -- the correlations can only be verified by comparing measurements via classical communication.
  • Entanglement does NOT mean the particles influence each other -- it means the system has correlated outcomes that were established when the entanglement was created.

Key takeaways

  • Entangled states cannot be described as products of individual qubit states.
  • Bell's theorem proves entanglement correlations exceed what local hidden variable theories can explain.
  • Entanglement is the key quantum resource for computational speedup, teleportation, and cryptography.

Check your understanding

Which of the following is an entangled state?

  1. A.|00⟩
  2. B.|+⟩|0⟩
  3. C.(|00⟩+|11⟩)/sqrt(2)
  4. D.|0⟩|1⟩
Show the answer

Answer: C. (|00⟩+|11⟩)/sqrt(2)

Why: (|00⟩+|11⟩)/sqrt(2) cannot be written as a product of individual qubit states, making it entangled. The other options are all product (separable) states.

Builds on

QubitSuperpositionQuantum MeasurementBell States

Primary source: Einstein, Podolsky & Rosen, Phys. Rev. 47, 777 (1935), doi:10.1103/PhysRev.47.777

Term per Schroedinger, Naturwissenschaften 23, 807 (1935); nonlocal correlations per Bell 1964.

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