Bell Inequality Violations Under Reasonable and Under Weak Hypotheses

Author(s)

de Faria, Edson ^[1] ; Tresser, Charles ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil

^[2] IBM Corp, Yorktown Hts, NY 10598 - USA

• Document type: Journal article
• Source: Physical Review Letters; v. 110, n. 26 JUN 28 2013.
• Web of Science Citations: 1

Abstract

Given a sequence of pairs (pi, (p) over bar (i)) of spin-1/2 particles in the singlet state, assume that Alice measures the normalized projections a(i) of the spins of the p(i)'s along vector a while Bob measures the normalized projections b(i) of the spins of the (p) over bar (i)'s along vector b. Then quantum mechanics (QM) lets one evaluate the correlation < a, b > as - cos(theta(a) - theta(b)) where theta(v) is the angle between the vector v and a reference vector chosen once and for all and in a fixed plane. Assuming classical microscopic realism (CMR) there exist also normalized projection pairs (a(i)', b(i)') of the spins of the pairs (p(i), (p) over bar (i)) along (a', b') so that < a', b'> = -cos(theta(a') - theta(b')). Since all projections are in [-1, 1], vertical bar < c, d > + < c, e >vertical bar + vertical bar < f, d > - < f, e >vertical bar <= 2 for c, d, e, and f in [a, b, a', b']. Assuming locality (the impossibility of any effect of an event on another event when said events are spatially separated) beside QM and CMR, Bell's theory lets one deduce various violations of this inequality at some choices of quadruplets Q = (a, b, a', b'). Our main result is the existence of such Q's where at least one of the above inequalities is violated if one only assumes QM, CMR, and some very mild further hypotheses that only concern the behavior of correlations that appear in these inequalities near special Q's. (AU)

• FAPESP's process: 06/03829-2 - Dynamic in low dimensions
• Grantee: André Salles de Carvalho
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 11/50128-8 - Charles Tresser | IBM - Estados Unidos
• Grantee: Edson de Faria
• Support Opportunities: Research Grants - Visiting Researcher Grant - International