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dc.contributor.authorGacs, Peteren_US
dc.date.accessioned2018-06-13T16:14:37Z
dc.date.available2018-06-13T16:14:37Z
dc.date.issued2001-09-07
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000171540700013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationP Gacs. 2001. "Quantum algorithmic entropy." Journal of Physics A: Mathematical and General, Volume 34, Number 35, pp. 6859 - 6880 (22).
dc.identifier.issn0305-4470
dc.identifier.urihttps://hdl.handle.net/2144/29383
dc.description.abstractWe extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (`universal probability') as a starting point, and define complexity (an operator) as its negative logarithm. A number of properties of Kolmogorov complexity extend naturally to the new domain. Approximately, a quantum state is simple if it is within a small distance from a low-dimensional subspace of low Kolmogorov complexity. The von Neumann entropy of a computable density matrix is within an additive constant from the average complexity. Some of the theory of randomness translates to the new domain. We explore the relations of the new quantity to the quantum Kolmogorov complexity defined by Vitányi (we show that the latter is sometimes as large as 2n − 2 log n) and the qubit complexity defined by Berthiaume, Dam and Laplante. The `cloning' properties of our complexity measure are similar to those of qubit complexity.en_US
dc.format.extentp. 6859 - 6880en_US
dc.languageEnglish
dc.publisherIOP PUBLISHING LTDen_US
dc.relation.ispartofJournal of Physics A: Mathematical and General
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectPhysics, mathematicalen_US
dc.subjectPhysicsen_US
dc.subjectMathematical aciencesen_US
dc.subjectMathematical physicsen_US
dc.titleQuantum algorithmic entropyen_US
dc.typeArticleen_US
dc.identifier.doi10.1088/0305-4470/34/35/312
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: No embargoen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Computer Scienceen_US
pubs.publication-statusPublisheden_US


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