Limitations on quantum dimensionality reduction

Ashley Montanaro, Aram W Harrow, A J Short

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

13 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationProceedings of ICALP'11
Publication statusPublished - 2011


Dive into the research topics of 'Limitations on quantum dimensionality reduction'. Together they form a unique fingerprint.

Cite this