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Improved bounds in the entropic uncertainty and certainty relations for complementary observables

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URI: https://hdl.handle.net/10016/6591
ISSN: 0375-9601
DOI: 10.1016/0375-9601(95)00219-S
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1995-05-22
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Elsevier
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The entropic uncertainty relation for sets of $N+1$ complementary observables $\{A_k\}$ in $N$-dimensional Hilbert space, $\sum_kH(A_k)\geq (N+1)\ln[\frac12(N+1)]$, is sharpened to $\sum_kH(A_k)\geq\frac12N\, \ln(\frac12N)+(\frac12 N+1)\!\ln(\frac12N+1)$ for even $N$. A nontrivial upper bound on the entropy sum (entropic certainty relation) is also obtained for not completely mixed states, while a previously given expression for this bound is proved to hold only when $N=2$.
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[MSC] Quantum measurement theory, [MSC] Quantum stochastic calculus
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Physics Letters A, 1995, vol. 201, n. 2-3, p. 125-131
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