Convex resource theory of non-Gaussianity
Name
PhysRevA.97.062337.pdf
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686.92 KB
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Adobe PDF
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07463adfa5b9569d276369cfed74632c
Author(s)
Takagi, Ryuji
Zhuang, Quntao
Date Issued
June 2018
Journal
Physical Review A
Publisher
American Physical Society
Citation
Takagi, Ryuji and Quntao, Zhuang. "Convex resource theory of non-Gaussianity." Physical Review A 97, 6 (June 2018): 062337 © 2018 American Physical Society
Version
Final published version
Abstract
Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations—Gaussian operations combined with feed-forward—are chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non-Gaussian states—states not in the convex hull of Gaussian states—are the necessary resource states for universal quantum computation together with free operations. We introduce a monotone to quantify the genuine non-Gaussianity of resource states, in analogy to the stabilizer theory. A direct application of our resource theory is to bound the conversion rate between genuine non-Gaussian states. Finally, we give a protocol that probabilistically distills genuine non-Gaussianity—increases the genuine non-Gaussianity of resource states—only using free operations and postselection on Gaussian measurements, where our theory gives an upper bound for the distillation rate. In particular, the same protocol allows the distillation of cubic phase states, which enable universal quantum computation when combined with free operations.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.97.062337
