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

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URI: https://hdl.handle.net/10016/6595
ISSN: 1751-8113 (Print)
ISSN: 1751-8121 (Online)
ISSN: 10.1088/0305-4470/27/21/010
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1994-11
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IOP
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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 $N>3$.
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Entropic uncertainty relation, Complementary observables, [PACS] Quantum mechanics, [PACS] Linear algebra, [PACS] Matrix theory
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Journal of Physics A: Mathematical and Theoretical, 1994, vol. 27, n. 21, p. L843-L846
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