Bell’S Proof of Nonlocality

Sujit K Choudhary, Pankaj Agrawal

Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bell’s famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bell’s inequality. The alternative proofs of Bell’s theorem without using Bell’s inequality are known as “nonlocality without inequality (NLWI)” proofs. We review one such proof namely the Hardy’s proof which due to its simplicity and generality has been considered the best version of Bell’s theorem.

Federico Laudisa

Libby Heaney, Adán Cabello, Marcelo França Santos +1 more

Quantum nonlocality is typically assigned to systems of two or more well-separated particles, but nonlocality can also exist in systems consisting of just a single particle when one considers the subsystems to be distant spatial field modes. Single particle nonlocality has been confirmed experimentally via a bipartite Bell inequality. In this paper, we introduce an N -party Hardy-like proof of the impossibility of local elements of reality and a Bell inequality for local realistic theories in the case of a single particle superposed symmetrically over N spatial field modes (i.e. N qubit W state). We show that, in the limit of large N , the Hardy-like proof effectively becomes an all-versus-nothing (or Greenberger–Horne–Zeilinger (GHZ)-like) proof, and the quantum-classical gap of the Bell inequality tends to be the same as that in a three-particle GHZ experiment. We describe how to test the nonlocality in realistic systems.

S. P. Boughn

Zeng‐Bing Chen, Sixia Yu, Zhang, Yong-De +1 more

Although entanglement is widely recognized as one of the most fascinating characteristics of quantum mechanics, nonlocality remains to be a big labyrinth. The proof of existence of nonlocality is as yet not much convincing because of its strong reliance on Bell's theorem where the assumption of realism weakens the proof. We demonstrate that entanglement and quantum nonlocality are two equivalent aspects of the same quantum wholeness for spacelike separated quantum systems. This result implies that quantum mechanics is indeed a nonlocal theory and lays foundation of understanding quantum nonlocality beyond Bell's theorem.