# States of minimal joint uncertainty for complementary observables in three-dimensional Hilbert space

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 dc.contributor.author Sánchez-Ruiz, Jorge dc.date.accessioned 2010-01-22T16:01:30Z dc.date.available 2010-01-22T16:01:30Z dc.date.issued 1994-11 dc.identifier.bibliographicCitation Journal of Physics A: Mathematical and Theoretical, 1994, vol. 27, n. 21, p. L843-L846 dc.identifier.issn 1751-8113 (Print) dc.identifier.issn 1751-8121 (Online) dc.identifier.issn 10.1088/0305-4470/27/21/010 dc.identifier.uri http://hdl.handle.net/10016/6595 dc.description.abstract The entropic uncertainty relation for sets of $N+1$ complementary observables $\{A_r\}$ existing in $N$-dimensional Hilbert space, $\sum_r H(A_r) \geq (N+1) \ln((N+ 1)/2)$, is shown to be optimal in the case $N=3$ by explicit construction of the states for which equality holds. We prove that the lower bound cannot be attained when $N$ is even, and, on the basis of numerical calculation, this is conjectured to also be the case for odd $N>3$. dc.format.mimetype text/html dc.language.iso eng dc.publisher IOP dc.subject.other Entropic uncertainty relation dc.subject.other Complementary observables dc.subject.other [PACS] Quantum mechanics dc.subject.other [PACS] Linear algebra dc.subject.other [PACS] Matrix theory dc.title States of minimal joint uncertainty for complementary observables in three-dimensional Hilbert space dc.type article dc.type.review PeerReviewed dc.description.status Publicado dc.relation.publisherversion http://dx.doi.org/10.1088/0305-4470/27/21/010 dc.subject.eciencia Matemáticas dc.rights.accessRights openAccess
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