Holevo bound of entropic uncertainty 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.

Improved quantum entropic uncertainty relations

“…As reported in Ref. [37], if the quantum memory moves away from the black hole, the difference between the total uncertainty and B ploy + k QM k remains a constant, independent on the properties of the black hole.…”

Dynamical Measurement's Uncertainty in the Curved Space‐Time

“…To date, there have been some authors to explore the QMA-EUR under the various types of environment noises. [52][53][54] Notably, Zhang et al [55] recently investigated the dynamics of QMA-EUR when quantum memory is located near the event horizon of Garfinkle-Horowitz-Strominger dilation (GHS-dilation) black hole. [49] Up to now, the dynamical features of correlation and entanglement have been explored in the curved space-time.…”

Tighter Bound of Entropic Uncertainty under the Unruh Effect

“…Heisenberg's uncertainty principle, which bounds our ability to simultaneously predict the measurement outcomes for two non‐commuting observables of a quantum particle, is one of the most remarkable features of quantum physics . With the rising of quantum information theory, entropy measurements can be exploited to quantify uncertainties naturally.…”

“…Owning to the extensive applications in the field of quantum information, such as quantum randomness, quantum key distribution, entanglement witness, and quantum cryptography, EUR attracted a lot of people's attention and many researches had been proposed to enhance the lower bound of entropy uncertainty . Among many options, Holevo bound is an effective method and has a wide range of applications …”