Entanglement is the quantum property most radically different from classical experience. Two particles prepared in an entangled state have correlated properties: measuring one of the two, the state of the other collapses instantaneously in a correlated way, even if the two particles are very far apart. It is not that the properties were already decided and hidden: before the measurement neither of the two possesses a precise value — it is the measurement of one that fixes, at the same instant, also the fate of the other.

Principle — Entangled state of two photons

A source emits two photons in opposite directions, prepared so that their polarisation is always orthogonal. Measuring the polarisation of the first photon with a Polaroid at 0°:

  • if it passes, the first was polarised at 0°; then the second is polarised at 90°90°;
  • if it does not pass, the first was polarised at 90°90°; then the second is polarised at 0°.

The correlation is immediate: before the measurement neither of the two had a precise polarisation.

The strangeness lies entirely here. In a classical world, the perfect correlation would be explained by supposing that each photon carries with it, from the outset, a hidden “label” with its own polarisation. Quantum mechanics instead says that this label does not exist until it is measured: the state of the two photons is a non-separable whole, not the simple juxtaposition of two individual states.

Key formula

  • Entanglement == non-separable joint state of the two particles.
  • Correlations >> any local hidden-variable theory.
  • Measurement of one \Rightarrow collapse of the other.

Topics: Fisica quantistica Concepts: Entanglement · Fotone · Polarizzazione e legge di Malus

Related exercises: Raccordo Malus e singolo fotone · Problema — Polarizzatore e conteggio di fotoni · Problema — Collasso della funzione d’onda al polarizzatore