5,999 research outputs found
Determining the Continuous Family of Quantum Fisher Information from Linear Response Theory
The quantum Fisher information represents the continuous family of metrics on
the space of quantum states and places the fundamental limit on the accuracy of
quantum state estimation. We show that the entire family of the quantum Fisher
information can be determined from linear response theory through generalized
covariances. We derive the generalized fluctuation-dissipation theorem that
relates the linear response function to generalized covariances and hence
allows us to determine the quantum Fisher information from linear response
functions, which is experimentally measurable quantities. As an application, we
examine the skew information, which is one of the quantum Fisher information,
of a harmonic oscillator in thermal equilibrium, and show that the equality of
the skew information-based uncertainty relation holds.Comment: 8 pages, 1 figur
A volume inequality for quantum Fisher information and the uncertainty principle
Let be complex self-adjoint matrices and let be a
density matrix. The Robertson uncertainty principle gives a bound for the quantum
generalized covariance in terms of the commutators . The right side
matrix is antisymmetric and therefore the bound is trivial (equal to zero) in
the odd case .
Let be an arbitrary normalized symmetric operator monotone function and
let be the associated quantum Fisher information. In
this paper we conjecture the inequality that gives a
non-trivial bound for any natural number using the commutators . The inequality has been proved in the cases by the joint efforts
of many authors. In this paper we prove the case N=3 for real matrices
Uncertainty Relations
Uncertainty relations are inequalities representing the impossibility of simultaneous measurement in quantum mechanics. The most well-known uncertainty relations were presented by Heisenberg and Schrödinger. In this chapter, we generalize and extend them to produce several types of uncertainty relations
A unified approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information
Local quantum uncertainty and interferometric power have been introduced by
Girolami et al. in [1,2] as geometric quantifiers of quantum correlations. The
aim of the present paper is to discuss their properties in a unified manner by
means of the the metric adjusted skew information defined by Hansen in [3].Comment: submitted to Entrop
Covariance and Fisher information in quantum mechanics
Variance and Fisher information are ingredients of the Cramer-Rao inequality.
We regard Fisher information as a Riemannian metric on a quantum statistical
manifold and choose monotonicity under coarse graining as the fundamental
property of variance and Fisher information. In this approach we show that
there is a kind of dual one-to-one correspondence between the candidates of the
two concepts. We emphasis that Fisher informations are obtained from relative
entropies as contrast functions on the state space and argue that the scalar
curvature might be interpreted as an uncertainty density on a statistical
manifold.Comment: LATE
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