Doubly infinite separation of quantum information and communication

Zi-Wen Liu, Christopher Perry, Yechao Zhu, Dax Enshan Koh, Scott Aaronson
2016 Physical Review A  
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)] 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
more » ... cales 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.
doi:10.1103/physreva.93.012347 fatcat:uer6d3fslzfhdfekmbgrlx3bum