Information gap for classical and quantum communication in a Schwarzschild spacetime

Communication between a free-falling observer and an observer hovering above the Schwarzschild horizon of a black hole suffers from Unruh-Hawking noise, which degrades communication channels. Ignoring time dilation, which affects all channels equally, we show that for bosonic communication using single- and dual-rail encoding, the classical channel capacity reaches a finite value and the quantum coherent information tends to zero. We conclude that classical correlations still exist at infinite acceleration, whereas the quantum coherence is fully removed.

Figure 1

Fidelity between the logical zero and one states received by Rob as a function of the acceleration $a$ for single- and dual-rail qubits.

Figure 2

Mutual information as a function of the acceleration $a$ when ${\left|\alpha \right|}^2={\left|\beta \right|}^2=\frac{1}{2}$.

Figure 3

Conditional entropy as a function of the acceleration $a$ when ${\left|\alpha \right|}^2={\left|\beta \right|}^2=\frac{1}{2}$.

Figure 4

The channel capacity $C$ as a function of the acceleration $a$ when ${\left|\alpha \right|}^2={\left|\beta \right|}^2=\frac{1}{2}$. The figure does not take into account relativistic time dilation, which reduces all communication rates to zero equally. While the classical channel capacity reaches a finite value at the Schwarzschild horizon, the quantum coherent information (also measured in bits) drops to zero. Dual-rail encoding outperforms single-rail encoding in both classical and quantum communication.