How can one distinguish, in the laboratory, a world with “hidden labels” from a truly quantum world? In 1964 John Bell wrote an inequality that every local hidden-variable theory must satisfy. Quantum mechanics, instead, predicts that it is violated — and the difference is measurable.

For an entangled two-photon system, with the polariser oriented at three angles 0, θ, 2θ0,\ \theta,\ 2\theta, a classical prediction based on local hidden variables imposes a ceiling on the correlations: local hidden variables:S2,\text{local hidden variables:} \quad S \leq 2, while quantum mechanics predicts a higher value: quantum mechanics:S=222,83.\text{quantum mechanics:} \quad S = 2\sqrt{2} \approx 2{,}83.

The real experiments — Aspect 1982, Hensen 2015 — measure the quantum value with very high precision: nature violates Bell’s inequality. Classical “local realism”, however intuitive, is simply false; entanglement is a real phenomenon (Kumar 2010).

Applications of entanglement

Since the 1990s entanglement has moved out of philosophical debates to become the resource of a new generation of technologies:

  • Quantum cryptography: protocols such as BB84 (1984) use entangled photons to generate intrinsically secure keys — any interception disturbs the state in a detectable way.
  • Quantum computing: entangled qubits allow operations in superposition that exponentially outperform classical computers for certain problems (Shor’s factorisation, Grover’s search, simulation of quantum systems).
  • Quantum teleportation: transferring the state of a photon from Alice to Bob destroys the original and reconstructs an identical state at the receiver. This has already been achieved over intercontinental distances via satellite (Micius, China, 2017).

Topics: Fisica quantistica Concepts: Entanglement

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