Relativistic quantum nonlocality for the three-qubit Greenberger-Horne-Zeilinger state

We study the effects of Lorentz transformations on three-particle non-local system states (GHZ and W) of spin 1/2 particles, using the Pauli spin operator and a three-particle generalization of Bell's inequality, introduced by Svetlichny. In our setup, the moving and laboratory frames used the (same) set of measurement directions that maximally violate Svetlichny's inequality in the laboratory frame. We also investigate the behavior of Mermin's and Collins' inequalities. We find that, regardless of the particles' type of entanglement, violation of Svetlichny's inequality in the moving frame is decreased by increasing the boost velocity and the energy of particles in the laboratory frame. In the relativistic regime Svetlichny's inequality is a good criterion to investigate the non-locality of the GHZ state. We also find that Mermin's and Collins' inequalities lead to reasonable predictions, in agreement with the behavior of the spin state, about non-locality of the W state in the relativistic regime. Then, comparing our results with those in which Czachor's relativistic spin is used instead of the Pauli operator, we find that the results obtained by considering the Pauli spin operator are in better agreement with the behavior of spin state of the system in the relativistic information theory.Comment: Accepted for QIN

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“…Here, we used the |S v | inequality and get the similar results as obtained in the references [47,48,64,66,83]. Therefore, based on Eqs.…”

Section: E(a Bc) = E(ab C) = E(abc ) = −E(a B C)mentioning

confidence: 85%

Three-particle Bell-like inequalities under Lorentz transformations

Moradpour

Maghool

Moosavi

2015

Quantum Inf Process

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“…(18) reduces to the S frame result (4 √ 2) in the appropriate limit of β → 0 and Ω p → 0. In the ultra-relativistic limit (β → 1) and independently of the particles' initial energy, unlike [54,57,58], all of the above inequalities are satisfied, indicating the familiar result that Bell's inequalities are satisfied in S ′ as β → 1 [22]. Now, let us point to the behavior of |S v | when Pauli's operator is considered instead of Czachor's.…”

Section: Three-partite Non-local System Under Ltmentioning

confidence: 91%

“…Author in [54] has used the |M | inequality and studied the relativistic behavior of the entanglement of GHZ state, when moving observer (S ′ ) uses measurements angles same as lab frame (S). He has used Czachor's relativistic spin operator [55] and considered a special set of measurement apparatus that violates the |M | inequality to its maximum possible value in the rest frame.…”

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confidence: 99%

Relativistic three-partite non-locality

Moradpour

Montakhab

2016

Int. J. Quantum Inform.

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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 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 GHZ states which exhibit distinctly different type of entanglement. We discuss the various types of three-particle 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 ($S^{\prime}$), 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 $v \rightarrow c$ limit. This is shown for both the GHZ and W states and in two different configurations which are commonly studied (\textbf{Case $I$} and \textbf{Case $II$}). 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 $v\rightarrow c$ 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.....Comment: Accepted version (Int. J. Quant. Info

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“…Finally |GHZ is the Lorentz transformed GHZ-state [7] |GHZ = 1 √ 2 (g 1 |000 + g 2 |001 + g 3 |010 + g 4 |011…”

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confidence: 99%

Frame Independent Nonlocality for Three Qubit State

Moradi

Aghaee

2010

Int J Theor Phys

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Bell's inequality is investigated for the three qubit GHZ state in relativistic regime. Two different relativistic spin operator are considered. One of them is defined by Lee and Ee (New J. Phys. 6:67, 2004). and the other which is the Pauli-Lubanski pseudovector used by Kim and Son (Phys. Rev. A 71:014102, 2005). It is shown that for both spin operator Bell's inequality is still maximally violated in a Lorentz-boosted frame.Keywords Bell's inequality · Relativistic spin operator An important resource for quantum communication and computation is entanglement. Recently, there has been much interest in the study of entanglement for inertial observers [1-9]. Ahn et al.[4] calculated the Bell observable for the Bell states under Lorentz boost and showed that the Bell's inequality is not violated in the relativistic limit. They used the relativistic spin observable which is closely related to the spatial components of the PauliLubanski pseudovector [5] and transformed the state under Lorentz boost accordingly. Their results strongly suggested that the entanglement is not preserved under the Lorentz boost. Lee et al. [1] showed that maximal violation of the Bell's inequality can be achieved by properly adjusting the directions of the spin measurement even in a relativistically moving inertial frame. Kim et al. [2] obtained an observer-independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame. They showed that the Bell observable and Bell states for Bell's inequality should be transformed following the principle of relativistic covariance, which results in a frame independent Bell's inequality. Moradi et al. [7] studied the Bell's inequality for three-qubit GHZ state in relativistic frame using the Czachor's spin operator. In this paper we would like to investigate the Bell's inequality for three particle states using two spin operators introduced in references [1] and [2] and show that relativistic invariant Bell's inequality can be achieved.

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Relativistic quantum nonlocality for the three-qubit Greenberger-Horne-Zeilinger state

Cited by 16 publications

References 21 publications

Three-particle Bell-like inequalities under Lorentz transformations

Three-particle Bell-like inequalities under Lorentz transformations

Relativistic three-partite non-locality

Frame Independent Nonlocality for Three Qubit State

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