284 research outputs found
Relativistic Einstein-Podolsky-Rosen correlation and Bell's inequality
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 is deteriorated 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 the 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. We must take account of this
relativistic effect in utilizing in moving frames the EPR correlation and the
violation of Bell's inequality for quantum communication.Comment: 33 pages, 6 figure
Simplicial Ricci Flow
We construct a discrete form of Hamilton's Ricci flow (RF) equations for a
d-dimensional piecewise flat simplicial geometry, S. These new algebraic
equations are derived using the discrete formulation of Einstein's theory of
general relativity known as Regge calculus. A Regge-Ricci flow (RRF) equation
is naturally associated to each edge, L, of a simplicial lattice. In defining
this equation, we find it convenient to utilize both the simplicial lattice, S,
and its circumcentric dual lattice, S*. In particular, the RRF equation
associated to L is naturally defined on a d-dimensional hybrid block connecting
with its (d-1)-dimensional circumcentric dual cell, L*. We show that
this equation is expressed as the proportionality between (1) the simplicial
Ricci tensor, Rc_L, associated with the edge L in S, and (2) a certain volume
weighted average of the fractional rate of change of the edges, lambda in L*,
of the circumcentric dual lattice, S*, that are in the dual of L. The inherent
orthogonality between elements of S and their duals in S* provide a simple
geometric representation of Hamilton's RF equations. In this paper we utilize
the well established theories of Regge calculus, or equivalently discrete
exterior calculus, to construct these equations. We solve these equations for a
few illustrative examples.Comment: 34 pages, 10 figures, minor revisions, DOI included: Commun. Math.
Phy
Entanglement of two qubits in a relativistic orbit
The creation and destruction of entanglement between a pair of interacting
two-level detectors accelerating about diametrically opposite points of a
circular path is investigated. It is found that any non-zero acceleration has
the effect of suppressing the vacuum entanglement and enhancing the
acceleration radiation thereby reducing the entangling capacity of the
detectors. Given that for large accelerations the acceleration radiation is the
dominant effect, we investigate the evolution of a two detector system
initially prepared in a Bell state using a perturbative mater equation and
treating the vacuum fluctuations as an unobserved environment. A general
function for the concurrence is obtained for stationary and symmetric
worldlines in flatspace. The entanglement sudden death time is computed.Comment: v2: Some typo's fixed, figures compressed to smaller filesize and
added some references
Quantum Entanglement and Teleportation in Higher Dimensional Black Hole Spacetimes
We study the properties of quantum entanglement and teleportation in the
background of stationary and rotating curved space-times with extra dimensions.
We show that a maximally entangled Bell state in an inertial frame becomes less
entangled in curved space due to the well-known Hawking-Unruh effect. The
degree of entanglement is found to be degraded with increasing the extra
dimensions. For a finite black hole surface gravity, the observer may choose
higher frequency mode to keep high level entanglement. The fidelity of quantum
teleporation is also reduced because of the Hawking-Unruh effect. We discuss
the fidelity as a function of extra dimensions, mode frequency, black hole mass
and black hole angular momentum parameter for both bosonic and fermionic
resources.Comment: 15 pages, 10 figures,contents expande
Matter waves in a gravitational field: An index of refraction for massive particles in general relativity
We consider the propagation of massive-particle de Broglie waves in a static,
isotropic metric in general relativity. We demonstrate the existence of an
index of refraction that governs the waves and that has all the properties of a
classical index of refraction. We confirm our interpretation with a WKB
solution of the general-relativistic Klein-Gordon equation. Finally, we make
some observations on the significance of the optical action.Comment: 20 pages, latex, ps and pdf. To appear in Am.J.Phys September, 200
Relativistic Quantum Games in Noninertial Frames
We study the influence of Unruh effect on quantum non-zero sum games. In
particular, we investigate the quantum Prisoners' Dilemma both for entangled
and unentangled initial states and show that the acceleration of the
noninertial frames disturbs the symmetry of the game. It is shown that for
maximally entangled initial state, the classical strategy C (cooperation)
becomes the dominant strategy. Our investigation shows that any quantum
strategy does no better for any player against the classical strategies. The
miracle move of Eisert et al (1999 Phys. Rev. Lett. 83 3077) is no more a
superior move. We show that the dilemma like situation is resolved in favor of
one player or the other.Comment: 8 Pages, 2 figures, 2 table
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