Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published July 2014 | Submitted
Book Section - Chapter Open

Variations on classical and quantum extractors

Abstract

Many constructions of randomness extractors are known to work in the presence of quantum side information, but there also exist extractors which do not [Gavinsky et al., STOC'07]. Here we find that spectral extractors with a bound on the second largest eigenvalue - considered as an operator on the Hilbert-Schmidt class - are quantum-proof. We then discuss fully quantum extractors and call constructions that also work in the presence of quantum correlations decoupling. As in the classical case we show that spectral extractors are decoupling. The drawback of classical and quantum spectral extractors is that they always have a long seed, whereas there exist classical extractors with exponentially smaller seed size. For the quantum case, we show that there exists an extractor with extremely short seed size d = O(log(1/ε)), where ε > 0 denotes the quality of the randomness. In contrast to the classical case this is independent of the input size and min-entropy and matches the simple lower bound d ≥ log(1/ε).

Additional Information

© 2014 IEEE. We acknowledge discussions with Stephanie Wehner. MB and VBS acknowledges financial support by the German Science Foundation (grant CH 843/2-1), the Swiss National Science Foundation (grants PP00P2-128455, 20CH21-138799 (CHIST-ERA project CQC)), the Swiss National Center of Competence in Research 'Quantum Science and Technology (QSIT), and the Swiss State Secretariat for Education and Research supporting COST action MP1006. The research of OF is supported by the European Research Council grant No. 258932. VBS is supported by an ETH Postdoctoral Fellowship.

Attached Files

Submitted - 1402.3279v1.pdf

Files

1402.3279v1.pdf
Files (164.2 kB)
Name Size Download all
md5:c09e487d0684e91a514758c03d48567c
164.2 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
October 20, 2023