Document Type
Article
Publication Date
12-1-2013
Abstract
We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level. We obtain a one-shot characterization of the minimum qubit compression size for an entanglement-assisted quantum rate-distortion code in terms of the smooth max-information, a quantity previously employed in the one-shot quantum reverse Shannon theorem. Next, we show how this characterization converges to the known expression for the entanglement-assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source. Finally, we give a tight, finite blocklength characterization for the entanglement-assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbolwise distortion constraint. © 1963-2012 IEEE.
Publication Source (Journal or Book title)
IEEE Transactions on Information Theory
First Page
8057
Last Page
8076
Recommended Citation
Datta, N., Renes, J., Renner, R., & Wilde, M. (2013). One-shot lossy quantum data compression. IEEE Transactions on Information Theory, 59 (12), 8057-8076. https://doi.org/10.1109/TIT.2013.2283723