69 research outputs found
Schr\"odinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure
In this paper, we give a Schr\"odinger-type uncertainty relation using the
Wigner-Yanase-Dyson skew information. In addition, we give Schr\"odinger-type
uncertainty relation by use of a two-parameter extended correlation measure.
Moreover, we give the further generalization for Schr\"odinger-type uncertainty
relation by metric adjusted correlation measure. These results generalize our
previous result in [Phys. Rev. A, Vol.82(2010), 034101].Comment: Section 3 was revise
Uncertainty Relations Based on Modified Wigner-Yanase-Dyson Skew Information
Uncertainty relation is a core issue in quantum mechanics and quantum
information theory. We introduce modified generalized Wigner-Yanase-Dyson
(MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson
(MWGWYD) skew information, and establish new uncertainty relations in terms of
the MGWYD skew information and MWGWYD skew information.Comment: 16 page
Tighter uncertainty relations based on modified weighted Wigner-Yanase-Dyson skew information of quantum channels
We use a novel formation to illustrate the () modified
weighted Wigner-Yanase-Dyson (() MWWYD) skew information
of quantum channels. By using operator norm inequalities, we explore the sum
uncertainty relations for arbitrary quantum channels and for unitary
channels. These uncertainty inequalities are shown to be tighter than the
existing ones by a detailed example. Our results are also applicable to the
modified weighted Wigner-Yanase-Dyson (MWWYD) skew information and the
() modified weighted Wigner-Yanase-Dyson (()
MWWYD) skew information of quantum channels as special cases.Comment: 12 pages, 2 figure
Schr\"odinger uncertainty relation with Wigner-Yanase skew information
We shall give a new Schr\"odinger type uncertainty relation for a quantity
representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our
result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a
mixed state.Comment: to appear in Phys.Rev.
A generalized skew information and uncertainty relation
A generalized skew information is defined and a generalized uncertainty
relation is established with the help of a trace inequality which was recently
proven by J.I.Fujii. In addition, we prove the trace inequality conjectured by
S.Luo and Z.Zhang. Finally we point out that Theorem 1 in {\it S.Luo and
Q.Zhang, IEEE Trans.IT, Vol.50, pp.1778-1782 (2004)} is incorrect in general,
by giving a simple counter-example.Comment: to appear in IEEE TI
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