Related papers: Three Lectures on Complexity and Black Holes
Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time…
We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann-Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability, we…
The quantum nature of a black hole is revealed using the simplest terms that one learns in undergraduate and beginning graduate courses. The exposition demonstrates -- vividly -- the importance and power of the quantum oscillator in…
The modeling of black holes is an important desideratum for any quantum theory of gravity. Not only is a classical black hole metric sought, but also agreement with the laws of black hole thermodynamics. In this paper, we describe how these…
Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric…
The thermodynamic properties of black holes have been extensively studied through analogies with classical systems, revealing fundamental connections between gravitation, entropy, and quantum mechanics. In this work, we extend the…
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are…
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with…
The formation and evaporation of two dimensional black holes are discussed. It is shown that if the radiation in minimal scalars has positive energy, there must be a global event horizon or a naked singularity. The former would imply loss…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
Black Holes are unique objects which allow for meaningful theoretical studies of strong gravity and even quantum gravity effects. An infalling and a distant observer would have very different views on the structure of the world. However, a…
We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to…
Fidelity and relative entropy are two significant quantities in quantum information theory. We study the quantum fidelity and relative entropy under unitary orbits. The maximal and minimal quantum fidelity and relative entropy between two…
An interesting question to explore in physics classes is whether gravity violates the second law of thermodynamics. Standard physics textbooks provide little to no discussion of the relationship between entropy and gravity, and the same is…
According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and…
Starting from a quantization relation for primordial extremal black holes with electric and magnetic charges, it is shown that their entropy is quantized. Furthermore the energy levels spacing for such black holes is derived as a function…
We describe how general covariance for QFT defined on a space-time background with horizons leads to the need of adding an extra quantum degree of freedom. The definition of traces and entropies involves the use of a formally thermal state…
In these lectures we explain the concept of supergravity p-branes and BPS black holes. Introducing an audience of general relativists to all the necessary geometry related with extended supergravity (special geometry, symplectic embeddings…
A deeper understanding of the thermal properties of black holes than we presently have depends to a large degree on obtaining a firmer grasp of the properties of the entropy. For such an understanding we must at least know the basic…
Here we discuss the two dimensional quantum electrodynamics in curved space-time, especially in the background of some black holes. We first show the existence of some new quantum mechanical solution which has interesting properties. Then…