Doubly infinite separation of quantum information and communication
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PhysRevA.93.012347.pdf
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Author(s)
Liu, Zi-Wen
Perry, Christopher
Zhu, Yechao
Koh, Dax Enshan
Aaronson, Scott
Date Issued
January 2016
Journal
Physical Review A
Publisher
American Physical Society
Citation
Liu, Zi-Wen, Christopher Perry, Yechao Zhu, Dax Enshan Koh, and Scott Aaronson. "Doubly infinite separation of quantum information and communication." Phys. Rev. A 93, 012347 (January 2016). © 2016 American Physical Society
Version
Final published version
Abstract
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call “doubly infinite,” between their quantum information and communication complexities. We do so by studying the exclusion game [C. Perry et al., Phys. Rev. Lett. 115, 030504 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.030504] for which there exist instances where the quantum information complexity tends to zero as the size of the input n increases. By showing that the quantum communication complexity of these games scales at least logarithmically in n, we obtain our result. We further show that the established lower bounds and gaps still hold even if we allow a small probability of error. However in this case, the n-qubit quantum message of the zero-error strategy can be compressed polynomially.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.93.012347
