Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0902.2366

Relativistic Einstein-Podolsky-Rosen Correlations in curved spacetime via Fermi-Walker Transport

K. Bakke, Alexandre M. de M. Carvalho, Claudio Furtado

Published Feb 13, 2009• 0 citations
arXivHTMLPDF

Abstract

We present a geometric description to study the relativistic EPR correlations in curved spacetime background given by the application of the Fermi-Walker transport in the relativistic EPR states and we show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi-Walker transport is equivalent to the expression demonstrated by Terashima and Ueda \cite{TU2}, where the degree of violation of the Bell inequality is dependent of the angle of the Wigner rotation. This geometrical approach to study the relativistic EPR correlations is a promissing formulation to investigate the EPR correlations in the general relativity background.

DOI
10.48550/arxiv.0902.2366

Related papers

RELATIVISTIC EINSTEIN–PODOLSKY–ROSEN CORRELATIONS IN COSMIC STRING SPACE–TIME VIA FERMI–WALKER TRANSPORT

K. Bakke, Alexandre M. de M. Carvalho, Claudio Furtado

We present a geometric approach to study the relativistic EPR correlations in curved space–time background given by the application of the Fermi–Walker transport in the relativistic EPR states and show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi–Walker transport is equivalent to the expression demonstrated by Terashima and Ueda,20 where the degree of violation of the Bell inequality depends on the angle of the Wigner rotation. This geometrical approach for study of the relativistic EPR correlations is a promising formulation to investigate the EPR correlations in the general relativity background.

International Journal of Quantum Information•Dec 1, 2010•11 citations

Wigner rotation via Fermi–Walker transport and relativistic EPR correlations in the Schwarzschild spacetime

K. Bakke, Claudio Furtado, Alexandre M. de M. Carvalho

The Wigner rotation angle for a particle in a circular motion in the Schwarzschild spacetime is obtained via the Fermi–Walker transport of spinors. Then, by applying the Wentzel, Kramers, Brillouin (WKB) approximation, a possible application of the Fermi–Walker transport of spinors in relativistic Einstein–Podolsky–Rosen (EPR) correlations is discussed, where it is shown that the spins of the correlated particle undergo a precession in an analogous way to that obtained by Terashima and Ueda [H. Terashima and M. Ueda, Phys. Rev. A 69, 032113 (2004)] via the application of successive infinitesimal Lorentz transformations. Moreover, from the WKB approach, it is also shown that the degree of violation of the Bell inequality depends on the Wigner rotation angle obtained via the Fermi–Walker transport. Finally, the relativistic effects from the geometry of the spacetime and the accelerated motion of the correlated particles is discussed in the nonrelativistic limit.

arXiv:1504.07432•International Journal of Quantum Information•Mar 1, 2015•7 citations

RELATIVISTIC EINSTEIN-PODOLSKY-ROSEN CORRELATION AND BELL'S INEQUALITY

Hiroaki Terashima, Masahito Ueda

We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction deteriorates in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. When considering moving frames we must take account of this relativistic effect on the EPR correlation and on the violation of Bell's inequality for quantum communication.

arXiv:quant-ph/0211177•International Journal of Quantum Information•Mar 1, 2003•102 citations

Strange behavior of the relativistic Einstein-Podolsky-Rosen correlations

Paweł Caban, Jakub Rembieliński, Marta Włodarczyk

We show that configurations exist in which the correlation functions and the degree of violation of Bell-type inequalities in the relativistic Einstein-Podolsky-Rosen (EPR) experiment have local extrema for some values of the velocities of the EPR particles. Moreover, this strange behavior can be observed for both discussed relativistic spin operators and for spin-$1∕2$ as well as spin-1 particles.

arXiv:0904.0918•Physical Review A•Jan 23, 2009•37 citations

Influence of the topology in EPR correlations

K. Bakke, Alexandre M. de M. Carvalho, Claudio Furtado

In this work, we verify the influence of the topology in Einstein–Podolsky–Rosen (EPR) correlations in the spacetime of a cosmic string. We show by means of a Wigner rotation that the presence of this topological defect breaks the spin anti-correlations of the EPR pairs. We also show that a perfect correlation can be obtained if we take into account the relativistic effect arising from the acceleration and the spacetime topology.

Journal of Physics A Mathematical and Theoretical•Jan 29, 2008•6 citations

Einstein-Podolsky-Rosen correlation in a gravitational field

Hiroaki Terashima, Masahito Ueda

For quantum communication in a gravitational field, the properties of the Einstein-Podolsky-Rosen (EPR) correlation are studied within the framework of general relativity. Acceleration and gravity are shown to deteriorate the perfect anticorrelation of an EPR pair of spins in the same direction, and apparently decrease the degree of the violation of Bell's inequality. To maintain the perfect EPR correlation and the maximal violation of Bell's inequality, observers must measure the spins in appropriately chosen different directions which depend on the velocity of the particles, the curvature of the space-time, and the positions of the observers. Near the event horizon of a black hole, the appropriate directions depend so sensitively on the positions of the observers that even a very small uncertainty in the identification of the observers' positions leads to a fatal error in quantum communication, unless the observers fall into the black hole together with the particles.

arXiv:quant-ph/0307114•Physical Review A•Mar 31, 2004•81 citations
We present a geometric description to study the relativistic EPR correlations in curved spacetime background given by the application of the Fermi-Walker transport in the relativistic EPR states and we show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi-Walker transport is equivalent to the expression demonstrated by Terashima and Ueda \cite{TU2}, where the degree of violation of the Bell inequality is dependent of the angle of the Wigner rotation. This geometrical approach to study the relativistic EPR correlations is a promissing formulation to investigate the EPR correlations in the general relativity background.
We present a geometric approach to study the relativistic EPR correlations in curved space–time background given by the application of the Fermi–Walker transport in the relativistic EPR states and show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi–Walker transport is equivalent to the expression demonstrated by Terashima and Ueda,20 where the degree of violation of the Bell inequality depends on the angle of the Wigner rotation. This geometrical approach for study of the relativistic EPR correlations is a promising formulation to investigate the EPR correlations in the general relativity background.
The Wigner rotation angle for a particle in a circular motion in the Schwarzschild spacetime is obtained via the Fermi–Walker transport of spinors. Then, by applying the Wentzel, Kramers, Brillouin (WKB) approximation, a possible application of the Fermi–Walker transport of spinors in relativistic Einstein–Podolsky–Rosen (EPR) correlations is discussed, where it is shown that the spins of the correlated particle undergo a precession in an analogous way to that obtained by Terashima and Ueda [H. Terashima and M. Ueda, Phys. Rev. A 69, 032113 (2004)] via the application of successive infinitesimal Lorentz transformations. Moreover, from the WKB approach, it is also shown that the degree of violation of the Bell inequality depends on the Wigner rotation angle obtained via the Fermi–Walker transport. Finally, the relativistic effects from the geometry of the spacetime and the accelerated motion of the correlated particles is discussed in the nonrelativistic limit.
We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction deteriorates in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. When considering moving frames we must take account of this relativistic effect on the EPR correlation and on the violation of Bell's inequality for quantum communication.
We show that configurations exist in which the correlation functions and the degree of violation of Bell-type inequalities in the relativistic Einstein-Podolsky-Rosen (EPR) experiment have local extrema for some values of the velocities of the EPR particles. Moreover, this strange behavior can be observed for both discussed relativistic spin operators and for spin-1∕21∕21∕2 as well as spin-1 particles.
For quantum communication in a gravitational field, the properties of the Einstein-Podolsky-Rosen (EPR) correlation are studied within the framework of general relativity. Acceleration and gravity are shown to deteriorate the perfect anticorrelation of an EPR pair of spins in the same direction, and apparently decrease the degree of the violation of Bell's inequality. To maintain the perfect EPR correlation and the maximal violation of Bell's inequality, observers must measure the spins in appropriately chosen different directions which depend on the velocity of the particles, the curvature of the space-time, and the positions of the observers. Near the event horizon of a black hole, the appropriate directions depend so sensitively on the positions of the observers that even a very small uncertainty in the identification of the observers' positions leads to a fatal error in quantum communication, unless the observers fall into the black hole together with the particles.