dc.contributor.author | Harrow, Aram W. | |
dc.contributor.author | Montanaro, Ashley | |
dc.contributor.author | Short, Anthony J. | |
dc.date.accessioned | 2015-08-07T13:56:33Z | |
dc.date.available | 2015-08-07T13:56:33Z | |
dc.date.issued | 2014-06 | |
dc.date.submitted | 2013-10 | |
dc.identifier.issn | 0219-7499 | |
dc.identifier.issn | 1793-6918 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/98056 | |
dc.description.abstract | The Johnson–Lindenstrauss Lemma is a classic result which implies that any set of n real vectors can be compressed to O(log n) dimensions while only distorting pairwise Euclidean distances by a constant factor. Here we consider potential extensions of this result to the compression of quantum states. We show that, by contrast with the classical case, there does not exist any distribution over quantum channels that significantly reduces the dimension of quantum states while preserving the 2-norm distance with high probability. We discuss two tasks for which the 2-norm distance is indeed the correct figure of merit. In the case of the trace norm, we show that the dimension of low-rank mixed states can be reduced by up to a square root, but that essentially no dimensionality reduction is possible for highly mixed states. | en_US |
dc.description.sponsorship | European Commission (Grant QESSENCE) | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research (United States. Defense Advanced Research Projects Agency. Microsystems Technology Office. Quantum Entanglement Science and Technology) | en_US |
dc.language.iso | en_US | |
dc.publisher | World Scientific | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1142/S0219749914400012 | en_US |
dc.rights | Creative Commons Attribution | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/ | en_US |
dc.source | International Journal of Quantum Information | en_US |
dc.title | Limitations on quantum dimensionality reduction | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Harrow, Aram W., Ashley Montanaro, and Anthony J. Short. “Limitations on Quantum Dimensionality Reduction.” Int. J. Quantum Inform. 13, no. 04 (June 2015): 1440001. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Center for Theoretical Physics | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Physics | en_US |
dc.contributor.mitauthor | Harrow, Aram W. | en_US |
dc.relation.journal | International Journal of Quantum Information | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Harrow, Aram W.; Montanaro, Ashley; Short, Anthony J. | en_US |
dc.identifier.orcid | https://orcid.org/0000-0003-3220-7682 | |
mit.license | PUBLISHER_CC | en_US |
mit.metadata.status | Complete | |