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 the results of using Czachor's and Pauli's operators to describe the spin entanglement and thus the system spin in relativistic information theory.
کلید واژگان :Multi-partite entanglement; Lorentz transformation
ارزش ریالی : 600000 ریال
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