Advantages and disadvantages of maximally entangled states in dilaton black hole background

TL;DR

The paper investigates how curved spacetime and Hawking radiation in a Garfinkle-Horowitz-Strominger dilaton black hole modify quantum resources carried by four classes of Bell-like fermionic states. The authors quantize a massless Dirac field in this background, build dilaton and Kruskal mode bases, and derive Bogoliubov transformations relating the two pictures, then trace over interior-horizon modes to obtain exterior states. They obtain analytic expressions for concurrence and two coherence measures, revealing that some non-maximally entangled states can outperform maximally entangled ones in entanglement under Hawking radiation, while coherence degrades monotonically with the dilaton. The study highlights resource-dependent state optimization for quantum information tasks in curved spacetime and clarifies how different coherence measures reflect distinct structural aspects of the states.

Abstract

We investigate quantum entanglement and coherence for four classes of Bell-like fermionic states in the vicinity of the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Contrary to the common expectation that maximally entangled states always provide superior quantum resources, our results show that their entanglement can be lower than that of suitably chosen non-maximally entangled states in this curved spacetime background. This reveals that non-maximally entangled states may offer operational advantages for entanglement-based tasks under gravitational effects. In contrast, quantum coherence exhibits monotonic behavior: larger initial coherence leads to systematically enhanced robustness against the dilaton induced degradation. These results indicate that the optimal choice of initial quantum states depends sensitively on the specific quantum resource, either quantum entanglement or quantum coherence, required for quantum information processing near a dilaton black hole.

Figures (3)

• Figure 1: Embedding diagram of the black hole and the detector configuration. Alice and Bob hover at fixed radial positions outside the event horizon, while the anti-Alice and anti-Bob modes correspond to the causally inaccessible region inside the event horizon.
• Figure 2: The concurrence $C(\rho^{{1},{\pm}}_{AB})$ and $C(\rho^{{2},{\pm}}_{AB})$, the $l_{1}$-norm of coherence $C_{\mathrm{l_{1}}}(\rho^{{1},{\pm}}_{AB})$ and $C_{\mathrm{l_{1}}}(\rho^{{2},{\pm}}_{AB})$, the REC $C_{\mathrm{REC}}(\rho^{{1},{\pm}}_{AB})$ and $C_{\mathrm{REC}}(\rho^{{2},{\pm}}_{AB})$ as functions of the dilaton $D$ for different initial parameters $\alpha$ with fixed $M = \omega_{A} = \omega_{B} = 1$.
• Figure 3: The concurrence $C(\rho^{{1},{\pm}}_{AB})$ and $C(\rho^{{2},{\pm}}_{AB})$, the $l_{1}$-norm of coherence $C_{\mathrm{l_{1}}}(\rho^{{1},{\pm}}_{AB})$ and $C_{\mathrm{l_{1}}}(\rho^{{2},{\pm}}_{AB})$, the REC $C_{\mathrm{REC}}(\rho^{{1},{\pm}}_{AB})$ and $C_{\mathrm{REC}}(\rho^{{2},{\pm}}_{AB})$ as functions of the dilaton $D$ for different initial parameters $\alpha$ with fixed $M = \omega_{A} = \omega_{B} = 1$.