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Volumn 36, Issue 9, 1995, Pages 4785-4791

Properties of q-entropies

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EID: 21844502823 PISSN: 00222488 EISSN: None Source Type: Journal
DOI: 10.1063/1.530920 Document Type: Article

Times cited : (78)

References (21)

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4
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- The quantum version (our Eq. (2)) of this formula is displayed on p. 247 of Wehrl’s excellent 1978 review who, of course
- Ref. 1

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- (1994)
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9
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- In infinite dimensions the congergence of [formula omitted] to 1 as [formula omitted] implies that [formula omitted] is divergent For negative q and in finite dimension [formula omitted] is given by (1) if ρ is non-degenerate (i.e., [formula omitted] for all j) otherwise it is [formula omitted] is then strictly convex on the interior of the simplex of probability distributions

10
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- Springer-Verlag, Berlin-Heidelberg
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12
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- The equality for disjoint probability measures is observed Eq. (7)
- Ref. 4

13
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14
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15
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- Cambridge University, Cambridge
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16
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- Assume [formula omitted] and suppose for simplicity that ρ is a pure state. Then [formula omitted] and ρ is a one-dimensional projection. Let [formula omitted] be a family of pairwise orthogonal one-dimensional projections such that [formula omitted] and put [formula omitted] for [formula omitted] where c is a positive real to be specified shortly. Let [formula omitted] where [formula omitted] If [formula omitted] then φ is a density operator with eigenvalues [formula omitted] and, since [formula omitted] we have [formula omitted] Moreover, [formula omitted] so that [formula omitted] which, for given [formula omitted] is not larger than ε as soon as [formula omitted]
- The argument of Ref. 2 works

17
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- This inequality provides us with an alternative proof of Lemma [formula omitted] and similarly for the other bound, because for [formula omitted] the operator norm [formula omitted] does not exceed 1

18
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- Extensive versus Nonextensive Physics
- The referee points out that this equation appears edited by J. L. Moran-Lopez and J. M. Sanchez(Plenum, New York)
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19
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- Doing Problem 1 on page 182 of Jauch’s book Addison-Wesley, Reading, MAyou will see that if [formula omitted] or [formula omitted] is pure, then [formula omitted]
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21
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- One can give simple examples for states ρ such that [formula omitted] for every [formula omitted] or alternatively, such that there is a [formula omitted] (necessarily [formula omitted] with [formula omitted] for every q such that [formula omitted] and [formula omitted] for all [formula omitted]
- This follows also directly from the fact that [formula omitted] is non-increasing (in fact strictly decreasing when ρ is not pure)

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