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quant-ph2010★ 16 cited
Limitations on quantum dimensionality reduction
Aram W. Harrow, Ashley Montanaro, Anthony J. Short
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 d…
quant-ph2010★ 37 cited
Testing product states, quantum Merlin-Arthur games and tensor optimisation
Aram W. Harrow, Ashley Montanaro
We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap w…