ECCC-Report TR16-016https://eccc.weizmann.ac.il/report/2016/016Comments and Revisions published for TR16-016en-usFri, 05 Feb 2016 12:46:21 +0200
Paper TR16-016
| Doubly infinite separation of quantum information and communication |
Zi-Wen Liu,
Christopher Perry,
Yechao Zhu,
Dax Enshan Koh,
Scott Aaronson
https://eccc.weizmann.ac.il/report/2016/016We 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)] 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.Fri, 05 Feb 2016 12:46:21 +0200https://eccc.weizmann.ac.il/report/2016/016