Quantum correlations through event horizons: Fermionic versus bosonic entanglement

We disclose the behavior of quantum and classical correlations among all the different spatial-temporal regions of a space-time with an event horizon, comparing fermionic with bosonic fields. We show the emergence of conservation laws for entanglement and classical correlations, pointing out the crucial role that statistics plays in the information exchange (and more specifically, the entanglement tradeoff) across horizons. The results obtained here could shed new light on the problem of information behavior in noninertial frames and in the presence of horizons, giving better insight into the black-hole information paradox.

Figure 1

Rindler space-time diagram: lines of constant position $z=\text{const}$ are hyperbolas, and all the curves of constant proper time $t$ for the accelerated observer are straight lines that come from the origin. A uniformly accelerated observer, Rob, travels along a hyperbola constrained to region I.

Figure 2

Dirac field: Mutual information tradeoff and conservation law between the Alice-Rob ($\mathit{AR}$, blue solid line) and Alice-AntiRob ($A\mathrm{R̄}$, red dotted line) systems as acceleration varies. It also shows the behavior of mutual information for the Rob-AntiRob system ($R\mathrm{R̄}$, black dashed line).

Figure 3

Same as Fig. 2, but showing negativity tradeoff and conservation law between the $\mathit{AR}$ and $A\mathrm{R̄}$ systems as acceleration varies, and the behavior of the quantum correlations for the $R\mathrm{R̄}$ system.

Figure 4

Scalar field: Mutual information tradeoff and conservation law between the $\mathit{AR}$ (blue solid line) and $A\mathrm{R̄}$ (red dashed line) systems.

Figure 5

Scalar field: Behavior of the mutual information for the $R\mathrm{R̄}$ system as acceleration varies.

Figure 6

Scalar field: Behavior of the negativity for the $\mathit{AR}$ bipartition as Rob accelerates.

Figure 7

Scalar field: Behavior of negativity for the bipartition Rob-AntiRob as Rob accelerates.

Figure 8

Scalar field: Comparison of growth of quantum and all (quantum+classical) correlations for the Rob-AntiRob system as acceleration increases. Quantum correlations are accounted for by logarithmic negativity (red dashed line). This figure compares this entanglement measurement with mutual information (blue solid line).