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Journal of Anhui University

Nonlocal correlative property of quantum state

XU Fu-xin

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

The nonlocality of quantum mechanics for generalized state of two spin 1/2 particles is proofed,this proof extend the Hardy's demonstration for two particles entangled state of Bell theorem and find the orthogonal condition of generalized quantum noncloning theorem for two particles entangled state can transfer from one particle to another one.

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Physical Review Letters•Mar 28, 1994•129 citations
The nonlocality of quantum mechanics for generalized state of two spin 1/2 particles is proofed,this proof extend the Hardy's demonstration for two particles entangled state of Bell theorem and find the orthogonal condition of generalized quantum noncloning theorem for two particles entangled state can transfer from one particle to another one.
The ladder proof of nonlocality without inequalities for two spin-12\frac{1}{2}21​ particles proposed by Hardy [in New Developments on Fundamental Problems in Quantum Physics, edited by M. Ferrero and A. van der Merwe (Kluwer, Dordrecht, 1997)] and Hardy and co-workers [Phys. Rev. Lett. 79, 2755 (1997)] works only for nonmaximally entangled states and goes through for 50% of pairs at the most. A similar ladder proof for two spin-111 particles in a maximally entangled state is presented. In its simplest form, the proof goes through for 17% of pairs. An extended version works for 100% of pairs. The proof can be extended to any maximally entangled state of two spin-sss particles (with s> 1)s>~1)s> 1).
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.
We provide a streamlined proof of Hardy's theorem, that almost every entangled state for a pair of quantum particles admits a ``proof of nonlocality'' without inequalities. Moreover, our analysis covers a larger class of observables. Thus we also strengthen Hardy's assertion that the argument fails for maximally entangled states, such as the singlet state. At the same time, we formulate the argument in such a manner that the relations which must be satisfied for local hidden variables are entirely deterministic, making no reference whatsoever to probability, let alone probablistic inequalities.