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dc.contributor.authorHarrow, Aram W.
dc.contributor.authorLin, Cedric Yen-Yu
dc.contributor.authorMontanaro, Ashley
dc.date.accessioned2019-12-03T16:13:37Z
dc.date.available2019-12-03T16:13:37Z
dc.date.issued2017-01
dc.identifier.isbn9781611974782
dc.identifier.urihttps://hdl.handle.net/1721.1/123101
dc.description.abstractWe describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and the case that all of the measurements have low probability of acceptance. The measurements cannot simply be tried in sequence, because early measurements may disturb the state being tested. One procedure is based on a variant of Marriott-Watrous amplification. The other procedure is based on the use of a test for this disturbance, which is applied with low probability. We find a number of applications:Quantum query complexity separations in the property testing model for testing isomorphism of functions under group actions. We give quantum algorithms for testing isomorphism, linear isomorphism and affine isomorphism of boolean functions which use exponentially fewer queries than is possible classically, and a quantum algorithm for testing graph isomorphism which uses polynomially fewer queries than the best algorithm known. Testing properties of quantum states and operations. We show that any finite property of quantum states can be tested using a number of copies of the state which is logarithmic in the size of the property, and give a test for genuine multipartite entanglement of states of n qubits that uses O(n) copies of the state. We also show that equivalence of two unitary operations under conjugation by a unitary picked from a fixed set can be tested efficiently. This is a natural quantum generalisation of testing isomorphism of boolean functions. Correcting an error in a result of Aaronson on demerlinizing quantum protocols. This result claimed that, in any one-way quantum communication protocol where two parties are assisted by an all-powerful but untrusted third party, the third party can be removed with only a modest increase in the communication cost. We give a corrected proof of a key technical lemma required for Aaronson's result.en_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/1.9781611974782.105en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSIAMen_US
dc.titleSequential measurements, disturbance and property testingen_US
dc.typeArticleen_US
dc.identifier.citationHarrow, Aram W. et al. “Sequential Measurements, Disturbance and Property Testing.” Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (January 2017) 1598-1611 © SIAMen_US
dc.contributor.departmentMassachusetts Institute of Technology. Center for Theoretical Physicsen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Physicsen_US
dc.relation.journalProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithmsen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-03-26T15:44:21Z
dspace.orderedauthorsHarrow, Aram W.; Lin, Cedric Yen-Yu; Montanaro, Ashleyen_US
dspace.embargo.termsNen_US
dspace.date.submission2019-04-04T11:28:14Z
mit.licensePUBLISHER_POLICYen_US


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