scholarly journals Taming singularities of the quantum Fisher information

2021 ◽  
Author(s):  
Aaron Z. Goldberg ◽  
José L. Romero ◽  
Ángel S. Sanz ◽  
Luis L. Sánchez-Soto
Keyword(s):  
Density Matrix ◽  
Fisher Information ◽  
Statistical Models ◽  
Probability Distributions ◽  
Quantum Fisher Information ◽  
Quantum Metrology ◽  
Quantum Statistical ◽  
Information Matrices ◽  
Parameter Dependent ◽  
Ultimate Limit

Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, forcing one away from the paradigm of regular statistical models. These questions of nonregular quantum statistical models are present in both single- and multiparameter estimation. Geometrically, singular QFIMs occur when the curvature of the metric vanishes in one or more directions in the space of probability distributions, while QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios, stressing the physical implications of singular QFIMs and the ensuing ramifications for quantum metrology.

About the quantum Fisher information of nearly pure quantum statistical models

2020 ◽  
Vol 18 (01) ◽  
pp. 1941022
Author(s):  
Matteo G. A. Paris
Keyword(s):  
Fisher Information ◽  
Statistical Models ◽  
Logarithmic Derivative ◽  
Quantum Fisher Information ◽  
Independent State ◽  
Approximate Analytic Expression ◽  
Weak Source ◽  
Pure States ◽  
Analytic Expression ◽  
Quantum Statistical

We address nearly pure quantum statistical models, i.e. situations where the information about a parameter is encoded in pure states weakly perturbed by the mixing with a parameter independent state, mimicking a weak source of noise. We show that the symmetric logarithmic derivative is left unchanged, and find an approximate analytic expression for the quantum Fisher information (QFI) which provides bounds on how much a weak source of noise may degrade the QFI.

Quantum Fisher information width in quantum metrology

2018 ◽  
Vol 62 (4) ◽  
Author(s):  
Bo Liu ◽  
GuoLong Li ◽  
YanMing Che ◽  
Jie Chen ◽  
XiaoGuang Wang
Keyword(s):  
Fisher Information ◽  
Quantum Fisher Information ◽  
Quantum Metrology

scholarly journals Remote State Design for Efficient Quantum Metrology with Separable and Non-Teleporting States

2021 ◽  
Vol 3 (1) ◽  
pp. 228-241
Author(s):  
Rahul Raj ◽  
Shreya Banerjee ◽  
Prasanta K. Panigrahi
Keyword(s):  
Parameter Estimation ◽  
Quantum Information ◽  
Fisher Information ◽  
Quantum Information Processing ◽  
Quantum Fisher Information ◽  
Quantum Correlations ◽  
Quantum States ◽  
Quantum Metrology ◽  
High Quantum ◽  
Non Local

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information.

scholarly journals Asymptotic inference in system identification for the atom maser

2012 ◽  
Vol 370 (1979) ◽  
pp. 5308-5323 ◽  
Author(s):  
Cătălin Cătană ◽  
Merlijn van Horssen ◽  
Mădălin Guţă
Keyword(s):  
System Identification ◽  
Fisher Information ◽  
Statistical Models ◽  
Quantum Fisher Information ◽  
Asymptotic Statistics ◽  
Quantum Dynamical ◽  
Process Tomography ◽  
Quantum Markov Processes ◽  
Set Up ◽  
Quantum Dynamical Systems

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

scholarly journals Symmetric Logarithmic Derivative of Fermionic Gaussian States

2018 ◽  
Author(s):  
Angelo Carollo ◽  
Bernardo Spagnolo ◽  
Davide Valenti
Keyword(s):  
Fisher Information ◽  
Logarithmic Derivative ◽  
Quantum Fisher Information ◽  
Closed Form Expression ◽  
Quantum Metrology ◽  
Many Body ◽  
Form Expression ◽  
Gaussian States ◽  
Many Body Systems ◽  
Thermal States

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

scholarly journals Quantum Fisher Information: Theory and Applications

2017 ◽  
Author(s):  
Volkan Erol
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Research Area ◽  
Quantum Metrology ◽  
Information Research ◽  
Active Research ◽  
Information Domain ◽  
Active Research Area

Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. QFI topic is a very active research area and it has many possible usage areas in quantum information domain. In this study, we review quantum Fisher information research with both from theoritical and application perspective.

scholarly journals Incompatibility in Multi-Parameter Quantum Metrology with Fermionic Gaussian States

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 34
Author(s):  
Angelo Carollo ◽  
Bernardo Spagnolo ◽  
Davide Valenti
Keyword(s):  
Fisher Information ◽  
Quantum Fisher Information ◽  
Spin Systems ◽  
Closed Form Expression ◽  
Quantum Metrology ◽  
Form Expression ◽  
Gaussian States ◽  
Optimal Measurement ◽  
Measurement Strategies ◽  
Thermal States

In this article we derive a closed form expression for the incompatibility condition in multi-parameter quantum metrology when the reference states are Fermionic Gaussian states. Together with the quantum Fisher information, the knowledge of the compatibility condition provides a way of designing optimal measurement strategies for multi-parameter quantum estimation. Applications range from quantum metrology with thermal states to non-equilibrium steady states with Fermionic and spin systems.

scholarly journals SUFFICIENCY IN QUANTUM STATISTICAL INFERENCE: A SURVEY WITH EXAMPLES

2006 ◽  
Vol 09 (03) ◽  
pp. 331-351 ◽  
Author(s):  
ANNA JENČOVÁ ◽  
DÉNES PETZ
Keyword(s):  
Statistical Inference ◽  
Fisher Information ◽  
Exponential Family ◽  
Weyl Algebra ◽  
Quantum Fisher Information ◽  
Quantum Statistics ◽  
Quantum Statistical ◽  
Basic Concepts ◽  
Noncommutative Analogue

This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated in parallel to the measure theoretic case. It turns out that several classical examples and results have a noncommutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related to the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result.

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