Fast Scramblers

Fast Scramblers

15 Aug 2008 | Yasuhiro Sekino^{1,2}, L. Susskind^{2}
The paper discusses the problem of how quickly a quantum system can scramble (thermalize) information, particularly focusing on systems with bounded clusters of degrees of freedom. The authors conjecture that: 1. The fastest scramblers take a time logarithmic in the number of degrees of freedom. 2. Matrix quantum mechanics saturates this bound. 3. Black holes are the fastest scramblers in nature. These conjectures are based on quantum information theory and the study of black holes in String Theory. The paper also explores the principle of Black Hole Complementarity, which suggests that no observer can detect the cloning of a quantum state, and provides a thought experiment involving Alice and Bob to illustrate this principle. The authors analyze the time required for information to be emitted from a black hole, showing that it scales at least as the scrambling time, which is logarithmic in the number of degrees of freedom. The paper further examines the scrambling time in various systems, including quantum circuits and D0-brane black holes, and uses the duality between 11-dimensional supergravity and M(atrix) Theory to estimate the scrambling time for black holes. It concludes that black holes are indeed fast scramblers, and this property is crucial for understanding the complementarity principle and the non-observability of quantum cloning.The paper discusses the problem of how quickly a quantum system can scramble (thermalize) information, particularly focusing on systems with bounded clusters of degrees of freedom. The authors conjecture that: 1. The fastest scramblers take a time logarithmic in the number of degrees of freedom. 2. Matrix quantum mechanics saturates this bound. 3. Black holes are the fastest scramblers in nature. These conjectures are based on quantum information theory and the study of black holes in String Theory. The paper also explores the principle of Black Hole Complementarity, which suggests that no observer can detect the cloning of a quantum state, and provides a thought experiment involving Alice and Bob to illustrate this principle. The authors analyze the time required for information to be emitted from a black hole, showing that it scales at least as the scrambling time, which is logarithmic in the number of degrees of freedom. The paper further examines the scrambling time in various systems, including quantum circuits and D0-brane black holes, and uses the duality between 11-dimensional supergravity and M(atrix) Theory to estimate the scrambling time for black holes. It concludes that black holes are indeed fast scramblers, and this property is crucial for understanding the complementarity principle and the non-observability of quantum cloning.
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