2018

Gluing polyhedra with entanglement in loop quantum gravity

Baytaş, Bekir, Bianchi, Eugenio, Yokomizo, Nelson

Understand

In a spin-network basis state, nodes of the graph describe un-entangled quantum regions of space, quantum polyhedra.

In this paper we show how entanglement between intertwiner degrees of freedom enforces gluing conditions for neighboring quantum polyhedra.
In particular we introduce Bell-network states, entangled states defined via squeezed vacuum techniques.
We study correlations of quantum polyhedra in a dipole, a pentagram and a generic graph.

Built on

T. Regge, General relativity without coordinates , Il Nuovo Cimento (1955-1965) 19
1961
Earlier work this paper cites.
R. Penrose Angular momentum: An approach to combinatorial space-time in Quantum Theory and Beyond, edited by T. Bastin (Cambridge University Press,Cambridge) (1971)
1971
Earlier work this paper cites.
R. Penrose On the Nature of Quantum Geometry, in: Magic Without Magic: J.A. Wheeler Festschrift, ed. J.R. Klauder, W.H.Freeman and Co Ltd (1973)
1973
Earlier work this paper cites.
T. Jacobson, Thermodynamics of space-time: The Einstein equation of state , Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
K. M. and M. J. J., The symplectic geometry of polygons in Euclidean space , J. Differential Geom. 44
1996
Earlier work this paper cites.
I. Montvay and G. Mn̈ster, Quantum fields on a lattice . Cambridge University Press, Cambridge, 1997
1997
Earlier work this paper cites.
A. Barbieri, Quantum tetrahedra and simplicial spin networks , Nucl. Phys. B518
1998
Earlier work this paper cites.
J. Roberts, Classical 6j-symbols and the tetrahedron , Geom. Topol. 3
1999
Earlier work this paper cites.
J. C. Baez and J. W. Barrett, The Quantum tetrahedron in three-dimensions and four-dimensions , Adv. Theor. Math. Phys. 3
1999
Earlier work this paper cites.
S. A. Major, Operators for quantized directions , Class. Quant. Grav. 16
1999
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information . Cambridge University Press, Cambridge, New York, 2000
2000
Earlier work this paper cites.
C. Rovelli, Quantum Gravity . Cambridge University Press, UK, 2004
2004
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski, Background independent quantum gravity: A status report , Class. Quant. Grav. 21
2004
Earlier work this paper cites.
F. Girelli and E. R. Livine, Reconstructing quantum geometry from quantum information: Spin networks as harmonic oscillators , Class. Quant. Grav. 22
2005
Earlier work this paper cites.
E. Bianchi, L. Modesto, C. Rovelli and S. Speziale, Graviton propagator in loop quantum gravity , Class. Quant. Grav. 23
2006
Earlier work this paper cites.
E. R. Livine and S. Speziale, Group Integral Techniques for the Spinfoam Graviton Propagator , JHEP 11
2006
Earlier work this paper cites.
T. Thiemann, Modern canonical quantum general relativity . Cambridge University Press, UK, 2007
2007
Earlier work this paper cites.
V. Aquilanti, H. M. Haggard, R. G. Littlejohn and L. Yu, Semiclassical Analysis of Wigner 3j-symbol , Journal of Physics A: Mathematical and Theoretical 40
2007
Earlier work this paper cites.

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Original
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Original
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Later among the works it cites.
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Original
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M. Han and M. Zhang, Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory , Class. Quant. Grav. 30
Original
2013
Later among the works it cites.
L. Freidel and J. Hnybida, On the exact evaluation of spin networks , J. Math. Phys. 54
Original
2013
Later among the works it cites.
C. Rovelli and F. Vidotto, Covariant Loop Quantum Gravity , Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2014
2014
Later among the works it cites.
E. Bianchi and R. C. Myers, On the Architecture of Spacetime Geometry , Class. Quant. Grav. 31
Original
2014
Later among the works it cites.
E. Bianchi, Loop Quantum Gravity a la Aharonov-Bohm , Gen. Rel. Grav. 46
Original
2014
Later among the works it cites.
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Original
2016
Later among the works it cites.
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Original
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T. Jacobson, Entanglement Equilibrium and the Einstein Equation , Phys. Rev. Lett. 116
Original
2016
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M. Saravani, S. Aslanbeigi and A. Kempf, Spacetime Curvature in terms of Scalar Field Propagators , Phys. Rev. D93
Original
2016
Later among the works it cites.
WSP, 2017
E. Bianchi, Spinfoam Gravity , in Loop Quantum Gravity: The First 30 Years (A. Ashtekar and J. Pullin, eds.) · 2017
Later among the works it cites.
C. Cao, S. M. Carroll and S. Michalakis, Space from Hilbert Space: Recovering Geometry from Bulk Entanglement , Phys. Rev. D95
Original
2017
Later among the works it cites.
E. R. Livine, Intertwiner Entanglement on Spin Networks , Phys. Rev. D97
2018
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