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dc.contributor.authorHarrow, Aram W.
dc.contributor.authorMontanaro, Ashley
dc.contributor.authorShort, Anthony J.
dc.date.accessioned2015-08-07T13:56:33Z
dc.date.available2015-08-07T13:56:33Z
dc.date.issued2014-06
dc.date.submitted2013-10
dc.identifier.issn0219-7499
dc.identifier.issn1793-6918
dc.identifier.urihttp://hdl.handle.net/1721.1/98056
dc.description.abstractThe 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.sponsorshipEuropean Commission (Grant QESSENCE)en_US
dc.description.sponsorshipUnited 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.isoen_US
dc.publisherWorld Scientificen_US
dc.relation.isversionofhttp://dx.doi.org/10.1142/S0219749914400012en_US
dc.rightsCreative Commons Attributionen_US
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/en_US
dc.sourceInternational Journal of Quantum Informationen_US
dc.titleLimitations on quantum dimensionality reductionen_US
dc.typeArticleen_US
dc.identifier.citationHarrow, 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.departmentMassachusetts Institute of Technology. Center for Theoretical Physicsen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Physicsen_US
dc.contributor.mitauthorHarrow, Aram W.en_US
dc.relation.journalInternational Journal of Quantum Informationen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsHarrow, Aram W.; Montanaro, Ashley; Short, Anthony J.en_US
dc.identifier.orcidhttps://orcid.org/0000-0003-3220-7682
mit.licensePUBLISHER_CCen_US
mit.metadata.statusComplete


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