A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

@article{Gibilisco2021AUA,
  title={A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information},
  author={Paolo Gibilisco and Davide Girolami and Frank Hansen},
  journal={Entropy},
  year={2021},
  volume={23}
}
Local quantum uncertainty and interferometric power were introduced by Girolami et al. 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 metric adjusted skew information defined by Hansen. 
View on PubMed
mdpi.com
3 Citations
Background Citations
1

Tables from this paper

3 Citations

Quantum Wasserstein distance based on an optimization over separable states

We define the quantum Wasserstein distance such that the optimization is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties.…

Quantifying coherence relative to channels via metric-adjusted skew information

A generalized Wigner–Yanase skew information

References

SHOWING 1-10 OF 33 REFERENCES

Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations

This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information to simplify the previously proposed proofs and lead to more general inequalities.

How to distinguish quantum covariances using uncertainty relations

Quantum Entanglement

  • M. Lewenstein
  • Physics, Computer Science
    Do We Really Understand Quantum Mechanics?
  • 2019
A brief overview of the concept of entanglement in quantum mechanics is given, and the major results and open problems related to the recent scientific progress in this field are discussed.

Advances in quantum metrology

The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root…

Inequalities for Quantum Skew Information

It is shown that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors.

Metrological Measures of Non-classical Correlations

In this work, we will review studies showing that non-classical, discord-like correlations do not necessarily describe a statistical dependence between measurements performed by non-communicating…

Inequalities for quantum Fisher information

In the paper [16] Luo proved an inequality relating the Wigner-Yanase information and the SLD-information. In this paper we prove that Luo’s inequality is a particular case of a general inequality…

Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations.

We introduce an infinite family of quantifiers of quantum correlations beyond entanglement which vanish on both classical-quantum and quantum-classical states and are in one-to-one correspondence…

Characterizing nonclassical correlations via local quantum uncertainty.

It is shown 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.

Quantum Discord Determines the Interferometric Power of Quantum States

Quantum metrology exploits quantum mechanical laws to improve the precision in estimating technologically relevant parameters such as phase, frequency, or magnetic fields. Probe states are usually…