Quantum Black Holes, Quantum Field Theory and Information Processing

Abstract

Black holes sit at the sharpest intersection of quantum mechanics, gravity, and statistical physics. Quantum theory demands unitary time evolution: a closed system evolves by a unitary operator and therefore preserves information. Classical general relativity, however, suggests that a black hole hides information behind an event horizon. Hawking’s discovery that black holes radiate [4, 5] turns this tension into a paradox: the Hawking quanta seen at infinity are thermal to leading order, so if the evaporation ends with no remnant, the outgoing radiation appears to be in a mixed state even when the initial state was pure. This is the black hole information paradox. Its modern form is not only a puzzle about where information goes, but a diagnostic of how semiclassical spacetime emerges from an underlying quantum theory of gravity. Over the last decade, quantum information theory has become the natural language for this diagnostic: entanglement entropy, mutual information, quantum channels, and quantum error correction provide model-independent constraints on how correlations can be distributed across subsystems. These constraints sharpen what semiclassical Hawking reasoning misses, and they guide the semiclassical gravitational computations that now reproduce unitary evaporation. For a comprehensive review of these developments, see [6]. A key theme of this thesis is that the information paradox is best understood as a mismatch of descriptions. The semiclassical effective theory describes quantum fields propagating on a fixed background geometry, while a microscopic theory describes the complete quantum state of black hole plus radiation. The paradox arises when we naively treat the effective description as if it were a faithful, isometric representation of the microscopic physics throughout the evaporation.