In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not allow an interpretation with local hidden variables. Quantum nonlocality has been experimentally verified under a variety of physical assumptions, with a notable exception being the many-worlds interpretation which violates an assumption of Bell's theorem. Quantum nonlocality does not allow for faster-than-light communication, and hence is compatible with special relativity and its universal speed limit of objects. Thus, quantum theory is local in the strict sense defined by special relativity and, as such, the term "quantum nonlocality" is sometimes considered a misnomer. Still, it prompts many of the foundational discussions concerning quantum theory.
History
Einstein, Podolsky and Rosen
In the 1935 EPR paper, Albert Einstein, Boris Podolsky and Nathan Rosen described "two spatially separated particles which have both perfectly correlated positions and momenta" as a direct consequence of quantum theory. They intended to use the classical principle of locality to challenge the idea that the quantum wavefunction was a complete description of reality, but instead they sparked a debate on the nature of reality. Afterwards, Einstein presented a variant of these ideas in a letter to Erwin Schrödinger, which is the version that is presented here. The state and notation used here are more modern, and akin to David Bohm's take on EPR. The quantum state of the two particles prior to measurement can be written as
| ψ A B ⟩ = 1 2 ( | 0 ⟩ A | 1 ⟩ B − | 1 ⟩ A | 0 ⟩ B ) = 1 2 ( | − ⟩ A | + ⟩ B − | + ⟩ A | − ⟩ B ) {\displaystyle \left|\psi _{AB}\right\rangle ={\frac {1}{\sqrt {2}}}\left(\left|0\right\rangle _{A}\left|1\right\rangle _{B}-\left|1\right\rangle _{A}\left|0\right\rangle _{B}\right)={\frac {1}{\sqrt {2}}}\left(\left|-\right\rangle _{A}\left|+\right\rangle _{B}-\left|+\right\rangle _{A}\left|-\right\rangle _{B}\right)}
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