Fast Scramblers

Fast Scramblers

15 Aug 2008 | Yasuhiro Sekino^{1,2}, L. Susskind^{2}
This paper explores the concept of quantum scrambling, the process by which information in a quantum system becomes thoroughly mixed and thermalized. The authors conjecture that the fastest scramblers are systems where the scrambling time is logarithmic in the number of degrees of freedom. They propose that matrix quantum mechanics, which describes systems with degrees of freedom as n×n matrices, saturates this bound. Additionally, they argue that black holes are the fastest scramblers in nature. The conjectures are supported by two main sources: quantum information theory and the study of black holes in string theory. The paper discusses the implications of black hole complementarity, a principle that suggests that information falling into a black hole is not lost but instead becomes encoded on the event horizon. The thought experiment involving Alice and Bob illustrates the potential contradiction between quantum mechanics and black hole complementarity, as it suggests that information could be cloned from Hawking radiation. The paper also examines the scrambling time in various systems, including quantum circuits and black holes. It shows that in quantum circuits, scrambling time scales logarithmically with the number of qubits, and in black holes, the scrambling time is related to the entropy of the black hole. The authors use the duality between 11-dimensional supergravity and matrix theory to estimate the scrambling time for D0-brane black holes, finding that it scales logarithmically with the number of degrees of freedom. The paper concludes that black holes are the fastest scramblers in nature, as they can scramble information in a time that is logarithmic in the number of degrees of freedom. This has important implications for the principle of black hole complementarity, as it suggests that information is not lost in a black hole but is instead scrambled and encoded on the event horizon. The results also support the idea that quantum information can be efficiently scrambled in systems with a large number of degrees of freedom, such as black holes.This paper explores the concept of quantum scrambling, the process by which information in a quantum system becomes thoroughly mixed and thermalized. The authors conjecture that the fastest scramblers are systems where the scrambling time is logarithmic in the number of degrees of freedom. They propose that matrix quantum mechanics, which describes systems with degrees of freedom as n×n matrices, saturates this bound. Additionally, they argue that black holes are the fastest scramblers in nature. The conjectures are supported by two main sources: quantum information theory and the study of black holes in string theory. The paper discusses the implications of black hole complementarity, a principle that suggests that information falling into a black hole is not lost but instead becomes encoded on the event horizon. The thought experiment involving Alice and Bob illustrates the potential contradiction between quantum mechanics and black hole complementarity, as it suggests that information could be cloned from Hawking radiation. The paper also examines the scrambling time in various systems, including quantum circuits and black holes. It shows that in quantum circuits, scrambling time scales logarithmically with the number of qubits, and in black holes, the scrambling time is related to the entropy of the black hole. The authors use the duality between 11-dimensional supergravity and matrix theory to estimate the scrambling time for D0-brane black holes, finding that it scales logarithmically with the number of degrees of freedom. The paper concludes that black holes are the fastest scramblers in nature, as they can scramble information in a time that is logarithmic in the number of degrees of freedom. This has important implications for the principle of black hole complementarity, as it suggests that information is not lost in a black hole but is instead scrambled and encoded on the event horizon. The results also support the idea that quantum information can be efficiently scrambled in systems with a large number of degrees of freedom, such as black holes.
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