• Fundamentals
  • Also: Bell nonlocality
  • Also: nonlocal correlations

Quantum Nonlocality

The property of quantum mechanics whereby entangled particles exhibit correlations that cannot be explained by any local hidden variable theory, as demonstrated by violations of Bell inequalities.

Quantum nonlocality is the experimental fact that entangled particles produce measurement correlations that exceed what any classical, locally realistic model can explain.

What it means

Two parties, Alice and Bob, share an entangled quantum state and make measurements at spacelike separation. The joint statistics of their outcomes can violate Bell inequalities — bounds on correlations derivable from any theory where:

  1. Locality: Alice’s outcome does not depend on Bob’s choice of measurement, and vice versa.
  2. Realism: Each particle has definite values for all measurable properties before measurement.

Together these are called local realism. Bell’s theorem (1964) proved that quantum mechanics predicts correlations incompatible with local realism for certain entangled states. The loophole-free Bell test experiments of 2015 (Delft, NIST, Vienna) closed the major experimental loopholes and confirmed: local realism is false.

The CHSH inequality

The most commonly tested Bell inequality is the CHSH inequality:

|S| = |⟨A₀B₀⟩ + ⟨A₀B₁⟩ + ⟨A₁B₀⟩ - ⟨A₁B₁⟩| ≤ 2

Classical (local realistic) theories satisfy |S| ≤ 2. Quantum mechanics predicts a maximum violation of S = 2√2 ≈ 2.828 for the optimal Bell state and measurement settings. This is the Tsirelson bound.

What it is not

Nonlocality does not allow faster-than-light communication. Alice and Bob’s individual outcomes are random; the nonlocal correlations only become visible when they compare results via classical communication. No information is transmitted by the correlations themselves.

Nonlocality also does not select a specific interpretation of quantum mechanics. It rules out local hidden variable theories but is compatible with many-worlds, Copenhagen, relational, and other interpretations.

Relevance to quantum computing

Quantum nonlocality underlies several quantum information protocols:

  • Quantum key distribution (QKD): Device-independent QKD uses Bell inequality violations to certify security without trusting the hardware.
  • Quantum games: The CHSH game can be won 85.4% of the time with entanglement vs 75% classically.
  • Entanglement witnesses: Bell inequality violations certify genuine entanglement without full state tomography.

See also