عنوان مجله
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INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
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چکیده
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Bell-like inequalities have been used in order to distinguish non-local quantum pure states by
various authors. The behavior of such inequalities under Lorentz transformation (LT) has been a
source of debate and controversies in the past. In this paper, we consider the two most commonly
studied three-particle pure states, that of W and Greenberger–Horne–Zeilinger (GHZ) states
which exhibit distinctly di®erent types of entanglement. We discuss the various types of threeparticle
inequalities used in previous studies and point to their corresponding shortcomings and
strengths. Our main result is that if one uses Czachor's relativistic spin operator and Svetlichny's
inequality as the main measure of non-locality and uses the same angles in the rest frame (S) as
well as the moving frame (S0), then maximally violated inequality in S will decrease in the
moving frame, and will eventually lead to lack of non-locality (i.e. satisfaction of inequality) in
the v ! c limit. This is shown for both the GHZ andWstates and in two di®erent con¯gurations
which are commonly studied (Cases 1 and 2). Our results are in line with a more familiar case of
two particle case. We also show that the satisfaction of Svetlichny's inequality in the v ! c limit
is independent of initial particles' velocity. Our study shows that whenever we use Czachor's
relativistic spin operator, results draws a clear picture of three-particle non-locality making its
general properties consistent with previous studies on two-particle systems regardless of the W
state or the GHZ state is involved. Throughout the paper, we also address the results of using
Pauli's operator in investigating the behavior of jSv
j under LT for both of the GHZ andWstates
and two cases (Cases 1 and 2). Our investigation shows that the violation of jSv
j in moving frame
depends on the particle's energy in the lab frame, which is in agreement with some previous
works on two and three-particle systems. Our work may also help us to classify
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