Supercritical entanglement in local systems: Counterexample to the area law for quantum matter
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Movassagh-2016-Supercritical entanglement in l.pdf
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Author(s)
Movassagh, Ramis
Shor, Peter Williston
Date Issued
November 2016
Journal
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences (U.S.)
Citation
Movassagh, Ramis and Shor, Peter W. “Supercritical Entanglement in Local Systems: Counterexample to the Area Law for Quantum Matter.” Proceedings of the National Academy of Sciences 113, no. 47 (November 2016): 13278–13282. © 2016 National Academy of Sciences
Version
Final published version
Abstract
Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an “area law”: The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system’s size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system’s size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1073/pnas.1605716113
