Leggett's theorem without inequalities

Abstract

We prove a no-go theorem for a class of hidden variables theories that satisfy parameter independence. Specifically, we show that, assuming two conditions, there are no non-trivial hidden variables models of the quantum predictions for product measurements on two systems in any maximally entangled state in a Hilbert space of dimension at least 3x3. The two conditions are parameter independence and a condition that we call conditional parameter independence. The result is analogous to the recent no-go theorems based on Leggett's inequalities and their generalisations.

13 pages. As compared to v1, this version includes the corrections in proof. Published in L. Accardi, G. Adenier, C. Fuchs, G. Jaeger, A. Yu. Khrennikov, J.-Å. Larsson and S. Stenholm (eds), Foundations of Probability and Physics-5, American Institute of Physics Conference Proceedings, Vol. 1101 (New York: AIP, 2009), pp. 233-240

References in corpus (3)

• Quantum entanglement can be simulated without communication
• Testing quantum correlations versus single-particle properties within Leggett's model and beyond
• Simulating quantum correlations as a distributed sampling problem