Relativistic quantum information
The application of quantum mechanics to relativistic contexts led to groundbreaking theoretical predictions, such as Hawking radiation and the Unruh effect. Since then, numerous models have been explored, aiming to uncover new and unexpected phenomena by incorporating quantum effects into curved spacetime. However, it is only in the past two decades that it has become evident that the fundamental principles of quantum mechanics must be revised to account for relativistic scenarios. This is where Relativistic Quantum Information (RQI) comes into play, a field focused on generalizing quantum information concepts for systems influenced by significant relativistic effects. These include, for instance, the interpretation of entanglement, the entropy, quantum causality structures, and quantum communication channels. RQI provides a more comprehensive extension of quantum principles within the framework of general relativity, bringing us closer to a unified theory of quantum gravity.
Relativistic quantum communication
The recent advancements in quantum technology and space science will soon necessitate reliable communication of quantum messages across large distances, even in dynamic spacetimes. Relativistic quantum communication focuses on predicting how gravitational fields or relative motion between communicating parties impact quantum communication protocols. A key focus of this research is the potential to enhance the quality of communication schemes through relativistic effects. At the same time, it aims to predict and mitigate noise introduced by relativistic scenarios to ensure the communication remains as clean as possible. Furthermore, communication protocols in this field can magnify quantum effects, typically minuscule in relativistic physics. Consequently, this research offers promising avenues for designing experimental setups that help bridge the gap between quantum mechanics and general relativity.
Entanglement Entropy in Curved Spacetime
Most readers are familiar with thermodynamic entropy, which is typically attributed to the lack of knowledge about the exact microstate corresponding to an observed macrostate. If a system of size \( V \) has a certain amount of thermodynamic entropy, then a new system composed of two identical copies of the original will have double the entropy. This property, known as the extensivity of entropy, implies that thermodynamic entropy scales with the system's volume.
In contrast to thermodynamic entropy, entanglement entropy is defined as the Von Neumann entropy of a quantum system and measures the entanglement between different parts of the system. Entanglement entropy cannot be attributed to a lack of knowledge about the system, as the quantum state encompasses all available information.
A key difference between the two types of entropy is their scaling behavior. For many quantum systems in their ground state, entanglement entropy scales with the surface area of the selected region rather than its volume. This phenomenon is known as the area law, which is particularly intriguing in theoretical physics due to its similarity to the Bekenstein-Hawking entropy of a black hole. This resemblance suggests that the entropy of a black hole may arise from the inaccessible quantum degrees of freedom within its interior.
In particular, we studied possible deviations from the area law in scenarios involving a quantum scalar field theory on curved spacetime. We began by examining whether a non-minimal Yukawa-like field-curvature coupling would affect the area law scaling and found that this interaction can indeed disrupt the linear behavior. We then considered models of quantum black holes, maintaining the non-minimal coupling, to understand the effect of enhanced regularity of the metric on entropy scaling. We observed deviations from the area law, particularly near the black hole origin.
Subsequently, we explored time-dependent scenarios by computing the entanglement entropy scaling during the formation of a black hole, as described by the Oppenheimer-Snyder model. In this case, we considered the field minimally coupled to the geometry. The area law is not strictly followed due to nonzero spatial curvature in the interior region. However, the deviations are minor in realistic star collapses.
This research aims to elucidate the role of entanglement entropy in quantum field theory within black holes, thereby providing insights into the interactions between gravity and quantum theory.