On upper bound for the quantum entropy
نویسندگان
چکیده
منابع مشابه
An Upper Bound on Quantum Entropy
Following ref [1], a classical upper bound for quantum entropy is identified and illustrated, 0 ≤ Sq ≤ ln(eσ/ 2~), involving the variance σ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Rényi.
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where 0 log 0 is taken as 0. Assume that the p~ are nonincreasing in n (reordering of the p~ does not affect H) . In a recent paper, Keilson (1971) showed that a sufficient condition for the series in (1) to be summable is that oo (i) Z1 P~ log n < ~ and (ii) P,.k ~ 1 / kp , as n ~ ~ for all fixed h = 1, 2 , . . . . I t will follow from the results given here that condition (i) alone is suffici...
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Let r > 1 and let Q be a probability measure on a measurable space (X, .4). In this note, we present a proof of a useful bound in Lr ( Q)-norm for the entropy of a convex hull in the case that covering numbers for a class of measurable functions are polynomial.
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We propose a method for upper bounding the general adversary bound for certain boolean functions. Due to the the tightness of query complexity and the general adversary bound [5], this gives an upper bound on the quantum query complexity of those functions. We give an example where this upper bound is smaller than the query complexity of any known quantum algorithm.
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A classical upper bound for quantum entropy is identified and illustrated, 0 ≤ Sq ≤ ln(eσ2/ 2~), involving the variance σ2 in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Rényi.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2001
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00244-0