Holevo Bound of Entropic Uncertainty in Schwarzschild Spacetime

TL;DR

This paper explores how quantum uncertainty bounds are affected by entanglement and curved spacetime near a black hole, demonstrating that the Holevo bound offers a tighter limit than previous measures in such scenarios.

Contribution

It introduces a new formulation of entropic uncertainty bounds in curved spacetime using the Holevo quantity, improving understanding of quantum information near black holes.

Findings

Holevo bound provides a tighter uncertainty limit than mutual information near black holes.

The difference between uncertainty and the Holevo bound remains constant when the memory moves away from the black hole.

The results apply specifically to Dirac fields in Schwarzschild spacetime.

Abstract

For a pair of incompatible quantum measurements, the total uncertainty can be bounded by a state-independent constant. However, such a bound can be violated if the quantum system is entangled with another quantum system (called memory); the quantum correlation between the systems can reduce the measurement uncertainty. On the other hand, in a curved spacetime, the presence of the Hawking radiation can increase the uncertainty in quantum measurement. The interplay of quantum correlation in the curved spacetime has become an interesting arena for studying quantum uncertainty relations. Here we demonstrate that the bounds of the entropic uncertainty relations, in the presence of memory, can be formulated in terms of the Holevo quantity, which limits how much information can be encoded in a quantum system. Specifically, we considered two examples with Dirac fields, near the event horizon of a Schwarzschild black hole, the Holevo bound provides a better bound than the previous bound based on the mutual information. Furthermore, if the memory moves away from the black hole, the difference between the total uncertainty and the Holevo bound remains a constant, not depending on any property of the black hole.