1,721,026 research outputs found
A characterisation of Wigner-Yanase skew information among statistically monotone metrics
Full text linkLet M-n = M-n(C) be the space of n x n complex matrices endowed with the Hilbert-Schmidt scalar product, let S-n be the unit sphere of M-n and let D-n subset of M-n be the space of strictly positive density matrices. We show that the scalar product over D-n introduced by Gibilisco and Isola(3) (that is the scalar product induced by the map D-n There Exists rho --> rootrho is an element of S-n) coincides with the Wigner-Yanase monotone metric
Uncertainty principle for Wigner Yanase Dyson information in semifinite von Neumann algebras
Full text linkIn Ref. 9, Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty principle in the semifinite case
An inequality related to uncertainty principle in von Neumann algebras
Full text linkRecently Kosaki proved an inequality for matrices that can be seen as a kind of new uncertainty principle. Independently, the same result was proved by Yanagi et al. The new bound is given in terms of Wigner-Yanase-Dyson informations. Kosaki himself asked if this inequality can be proved in the setting of von Neumann algebras. In this paper we provide a positive answer to that question and moreover we show how the inequality can be generalized to an arbitrary operator monotone function
Stam inequality on Z(n)
Full text linkWe prove a discrete version of Stam inequality for random variables taking values on Z(n
How to distinguish quantum covariances using uncertainty relations
No full textAbstractTo each operator monotone function it is possible to associate a quantum version of the classical covariance. We show that: i) only for regular quantum covariances one can prove non-trivial uncertainty relations; ii) the usual quantum covariance gives the best inequalities in this setting
Singular Traces on Semifinite von Neumann Algebras
No full textSingular traces are constructed on a general semifinite von Neumann algebra, thus generalizing the result of Dixmier (C.R. Acad. Sci. Paris 262, 1966.) Moreover our technique produces singular traces on type II1 factors. Such traces, though vanishing on all bounded operators, are non trivial on the *-algebra of affiliated unbounded operators. On a semifinite factor, we show that all traces are given by a dilation invariant functional on the cone of positive decreasing functions on [0, infinity), and we prove that the existence of a singular trace which is non trivial on a given operator is equivalent to an eccentricity condition on the singular values function, a result which generalizes the theorem given in (S. Albeverio, D. Guide, A. Ponosov, and S. Scarlatti, J. Funct. Anal., to appear.) for B(H). (C) 1995 Academic Press, Inc
On the characterisation of paired monotone metrics
Full text linkMonotone metrics, Wigner-Yanase-Dyson information,
Inequalities for quantum Fisher information
Full text linkAn inequality relating the Wigner-Yanase information and the SLD-quantum Fisher information was established by Luo (Proc. Amer. Math. Soc., 132, pp. 885-890, 2004). In this paper, we generalize Luo's inequality to any regular quantum Fisher information. Moreover, we show that this general inequality can be derived from the Kubo-Ando inequality, which states that any matrix mean is greater than the harmonic mean and smaller than the arithmetic mean
A Robertson-type Uncertainty Principle and Quantum Fisher Information
Full text linkLet A1,...,A(N) be complex self-adjoint matrices and let rho be a density matrix. The Robertson uncertainty principle det{Cov rho(A(h), A(j))} >= det{ -1/2Tr(rho[A(h), A(j)])} gives a bound for the quantum generalized variance in terms of the commutators [A(h), A(j)]. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case N = 2m + 1. Let f be an arbitrary normalized symmetric operator monotone function and let (.,.)(rho,f) be the associated quantum Fisher information. We have conjectured the inequality det{Cov rho(A(h), A(j))} >= det {f(0)/2 < i[rho, A(h)], i[rho, Aj]>rho,f} that gives a non-trivial bound for any N is an element of N using the commutators [rho, A(h)]. In the present paper the conjecture is proved by mean of the Kubo-Ando mean inequalit
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