Entanglement degradation in multi-event horizon spacetimes

Abstract

We investigate the degradation of quantum entanglement in the Schwarzschild-de Sitter black hole spacetime, by studying the mutual information and the logarithmic negativity for maximally entangled, bipartite states for massless minimal scalar fields. This spacetime is endowed with a black hole as well as a cosmological event horizon, giving rise to particle creation at two different temperatures. We consider two independent descriptions of thermodynamics and particle creation in this background. The first involves thermal equilibrium of an observer with either of the horizons. We show that as of the asymptotically flat/anti-de Sitter black holes, in this case the entanglement or correlation degrades with increasing Hawking temperatures. The second treats both the horizons combined in order to define a total entropy and an effective equilibrium temperature. We present a field theoretic derivation of this effective temperature and show that unlike the usual cases, the particle creation does not occur here in causally disconnected spacetime wedges but instead in a single region. Using the associated vacua, we show that in this scenario the entanglement never degrades but increases with increasing black hole temperature and holds true no matter how hot the black hole becomes or how small the cosmological constant is. We argue that this phenomenon can have no analogue in the asymptotically flat/anti-de Sitter black hole spacetimes.

v2, 9pp, 3 figures; Added references and many clarifications; Accepted in PRD; We dedicate this manuscript to late Prof. Thanu Padmanabhan

References in corpus (6)

• The Unruh effect and its applications
• Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime
• Degradation of non-maximal entanglement of scalar and Dirac fields in non-inertial frames
• Greybody Factors for Scalar Fields emitted by a Higher-Dimensional Schwarzschild-de-Sitter Black-Hole
• Black holes and Boyle's law -- the thermodynamics of the cosmological constant
• Thermodynamics of phase transition in higher dimensional Reissner-Nordström-de Sitter black hole

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• Decoherence and entropy generation in an open quantum scalar-fermion system with Yukawa interaction
• Quantumness near the Schwarzschild black hole based on W-state
• A dynamic theory of entanglement for uniformly accelerated atoms
• Tripartite quantum steering in Schwarzschild spacetime