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Volumn 9, Issue 7-8, 2009, Pages 0657-0665

Correlation loss and multipartite entanglement across a black hole horizon

Author keywords

Continuous variable correlations; Hawking Unruh effect; Multipartite entanglement; Schwarzschild black holes

Indexed keywords

ELECTRON ENERGY ANALYZERS; HIGH ENERGY PHYSICS; QUANTUM ENTANGLEMENT; STARS;

EID: 67651171383     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (30)

References (37)
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    • For reviews see: J. Preskill, arXiv:hep-th/9209058; S. Carlip, arXiv:0705.3024.
    • For reviews see: J. Preskill, arXiv:hep-th/9209058; S. Carlip, arXiv:0705.3024.
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  • 12
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    • Kruskal (Schwarzschild) observers are defined by the vector field ∂ u (∂ t), where u (t) is the Kruskal (Schwarzschild) temporal coordinate [9, 7]. A Kruskal (Schwarzschild) state/mode refers to the state/mode described by the respective observers.
    • Kruskal (Schwarzschild) observers are defined by the vector field ∂ u (∂ t), where u (t) is the Kruskal (Schwarzschild) temporal coordinate [9, 7]. A Kruskal (Schwarzschild) state/mode refers to the state/mode described by the respective observers.
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    • D. Ahn, Phys. Rev. D 74, 084010 (2006).
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  • 17
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    • In this respect we notice that the degradation of correlations in a different type of two-mode entangled Kruskal state, i.e. a two-qubit-like Bell state |00〉, 11〉, as detected by Schwarzschild observers, have been recently studied [14, However, in that case it was not possible to frame the effect of black hole within the theory of entanglement redistribution, nor a degradation of classical correlations was observable
    • In this respect we notice that the degradation of correlations in a different type of two-mode entangled Kruskal state, i.e. a two-qubit-like Bell state |00〉 + |11〉, as detected by Schwarzschild observers, have been recently studied [14]. However, in that case it was not possible to frame the effect of black hole within the theory of entanglement redistribution, nor a degradation of classical correlations was observable.
  • 20
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    • G. Adesso and F. Illuminati, Int. J. Quant. Inf 4, 383 (2006).
    • G. Adesso and F. Illuminati, Int. J. Quant. Inf 4, 383 (2006).
  • 21
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    • The entropy of entanglement of a bipartite state |ψ〉 AB is defined as S(ρ A) = S(ρ B) = -TR[ρ A log(ρ A)], where ρ A (ρ B) is the reduced density matrix of subsystem A (B).
    • The entropy of entanglement of a bipartite state |ψ〉 AB is defined as S(ρ A) = S(ρ B) = -TR[ρ A log(ρ A)], where ρ A (ρ B) is the reduced density matrix of subsystem A (B).
  • 24
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    • i|j = 1.
    • i|j = 1.
  • 27
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    • G. Adesso and F. Illuminati, ibid. 72, 032334 (2005)
    • G. Adesso and F. Illuminati, ibid. 72, 032334 (2005)
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    • G. Adesso, M. Ericsson, and F. Illuminati, Phys. Rev. A 76, 022315 (1007).
    • G. Adesso, M. Ericsson, and F. Illuminati, Phys. Rev. A 76, 022315 (1007).
  • 37
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    • An infinitely entangled state, accompanied by unbounded energy, is unphysical. The appearance of such states is a well known issue in black hole physics, and only a satisfactory theory of quantum gravity might be able to renormalize these divergences by properly describing the physics of a black hole close to evaporation. In fact, Hawking's semiclassical calculations [7] within the formalism of quantum field theory in curved spacetimes [9, break down at the Planck scale. We can then safely conclude that our results concerning correlation loss and entanglement redistribution are physical at least for black hole masses M above the Planck mass Mp, 1 (in natural units, This corresponds to introducing a cutoff on the radiated energy and thus on the distributed entanglement. Quantitatively, from Fig. 3 and Eq, 5) one can see that, e.g. setting λ, 1/ 8π, the four-partite entanglement at the Planck scale is τ res ≈
    • res ≈ 45 ebits for ξ = 3, and so on. It increases with increasing squeezing ξ and decreasing frequency λ.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.