Generalized Entanglement Entropies of Quantum Designs
Name
PhysRevLett.120.130502.pdf
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166.91 KB
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Adobe PDF
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Author(s)
Zhu, Huangjun
Liu, Zi-Wen
Lloyd, Seth
Zhu, Elton
Date Issued
March 2018
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Liu, Zi-Wen et al. "Generalized Entanglement Entropies of Quantum Designs." Physical Review Letters 120, 13 (March 2018): 130502 © 2018 American Physical Society
Version
Final published version
Abstract
The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Rényi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page’s theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Rényi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Rényi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.120.130502
