Wigner-Yanase skew information as tests for quantum entanglement

A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light on relationships between quantum entanglement and information theory.Comment: 5 page

Information geometry of density matrices and state estimation

Given a pure state vector |x> and a density matrix rho, the function p(x|rho)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived.Comment: published versio

Tighter uncertainty relations based on (α,β,γ)(\alpha,\beta,\gamma) modified weighted Wigner-Yanase-Dyson skew information of quantum channels

We use a novel formation to illustrate the ($\alpha,\beta,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha,\beta,\gamma$) MWWYD) skew information of quantum channels. By using operator norm inequalities, we explore the sum uncertainty relations for arbitrary $N$ 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 ($\alpha,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha,\gamma$) MWWYD) skew information of quantum channels as special cases.Comment: 12 pages, 2 figure

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

Tighter sum uncertainty relations via metric-adjusted skew information

In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special cases as Wigner-Yanase-Dyson skew information. In quantifying the uncertainty of channels, we discuss two types of lower bounds and compare the tightness between them, meanwhile, a tight lower bound is given. The uncertainty relations obtained by us are stronger than the existing ones. To illustrate our results, we give several specific examples.Comment: 17 pages, 4 figure

Characterizing Nonclassical Correlations via Local Quantum Uncertainty

Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide measures of nonclassical correlations. For the case of 2 x d systems, we find that a unique measure is defined, which we evaluate in closed form. We then discuss the role that these correlations, which are of the 'discord' type, can play in the context of quantum metrology. We show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision, as quantified by the quantum Fisher information, in the optimal phase estimation protocol.Comment: Published in PRL, Editors' Suggestio