Probably approximately correct quantum source coding
Abstract
Informationtheoretic lower bounds are often encountered in several branches of computer science, including learning theory and cryptography. In the quantum setting, Holevo's and Nayak's bounds give an estimate of the amount of classical information that can be stored in a quantum state. Previous works have shown how to combine informationtheoretic tools with a counting argument to lower bound the sample complexity of distributionfree quantum probably approximately correct (PAC) learning. In our work, we establish the notion of Probably Approximately Correct Source Coding and we show two novel applications in quantum learning theory and delegated quantum computation with a purely classical client. In particular, we provide a lower bound of the sample complexity of a quantum learner for arbitrary functions under the Zipf distribution, and we improve the security guarantees of a classicallydriven delegation protocol for measurementbased quantum computation (MBQC).
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 DOI:
 10.48550/arXiv.2112.06841
 arXiv:
 arXiv:2112.06841
 Bibcode:
 2021arXiv211206841A
 Keywords:

 Quantum Physics;
 Computer Science  Cryptography and Security;
 Computer Science  Information Theory;
 Computer Science  Machine Learning
 EPrint:
 13 pages, 1 figure