# Generalized measure of quantum Fisher information

@article{Sone2021GeneralizedMO, title={Generalized measure of quantum Fisher information}, author={Akira Sone and Mar{\'i}a Cerezo and Jacob L. Beckey and Patrick J. Coles}, journal={Physical Review A}, year={2021} }

In this work, we present an efficiently computable lower bound on the quantum Fisher information (QFI). This bound itself is of interest, as we show that it satisfies the canonical criteria of a QFI measure. Specifically, it is essentially a QFI measure for sub-normalized states, and hence it generalizes the standard QFI in this sense. Our bound employs the generalized fidelity applied to the truncated state, which is constructed via the $m$ largest eigenvalues and their corresponding…

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## References

SHOWING 1-10 OF 43 REFERENCES

### Quantum Information Processing with Finite Resources

- Mathematical Foundations,
- 2015

### Duality Between Smooth Min- and Max-Entropies

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2010

In this paper, a recently discovered duality relation between (nonsmooth) min- and max-entropies is extended to the smooth case and it is shown that the smooth min-entropy of a system A conditioned on a system B equals the negative of the smooth max-Entropy of Acondition on a purifying system C.

### Variational Quantum Algorithms

- Physics, Computer ScienceNature Reviews Physics
- 2021

An overview of the field of Variational Quantum Algorithms is presented and strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage are discussed.

### Variational quantum algorithm for estimating the quantum Fisher information

- Computer SciencePhysical Review Research
- 2022

A variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) is presented, which estimates lower and upper bounds on the QFI, based on bounding the fidelity, and outputs a range in which the actual QFI lies.

### A variational toolbox for quantum multi-parameter estimation

- Computer Science, Physicsnpj Quantum Information
- 2021

This work demonstrates that variational quantum algorithms feasible on such devices address a challenge central to the field of quantum metrology: the identification of near-optimal probes and measurement operators for noisy multi-parameter estimation problems.

### Quantum monotone metrics induced from trace non-increasing maps and additive noise

- Mathematics
- 2020

Quantum monotone metric was introduced by Petz,and it was proved that quantum monotone metrics on the set of quantum states with trace one were characterized by operator monotone functions. Later,…

### Geometric distinguishability measures limit quantum channel estimation and discrimination

- Computer ScienceQuantum Inf. Process.
- 2021

This paper introduces the amortized quantum Fisher information as a conceptual framework for analyzing general sequential protocols that estimate a parameter encoded in a quantum channel, and uses this framework to show that Heisenberg scaling is not possible when a parameter is encode in a classical-quantum channel.

### Variational quantum state eigensolver

- Computer Sciencenpj Quantum Information
- 2022

The variational quantum state eigensolver (VQSE) is introduced, which is analogous to VQE in that it variationally learns the largest eigenvalues of ρ as well as a gate sequence V that prepares the corresponding eigenvectors.

### Quantum Fisher information matrix and multiparameter estimation

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér–Rao bound in quantum parameter estimation. However,…

### Variational Quantum Fidelity Estimation

- Computer ScienceQuantum
- 2020

This work proposes novel lower and upper bounds for the fidelity F(ρ,σ) based on the ``truncated fidelity'' F(ν,σ), which is evaluated for a state ρm obtained by projecting ρ onto its m-largest eigenvalues, and introduces a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps.