Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1101.4659 · Physica A Statistical Mechanics and its Applications

Inferring an optimal Fisher measure

Silvana Flego, Angel Ricardo Plastino, Angel Ricardo Plastino

Published Jun 28, 2011• 9 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2011.06.050

Related papers

Uncertainty relations from Fisher information

Z. Hradil, Jaroslav Řeháček

Journal of Modern Optics•May 1, 2004•4 citations

Contextual quantum metrology

Jeongwoo Jae, Jiwon Lee, M. S. Kim +2 more

Abstract We demonstrate that the contextuality of measurement selection can enhance the precision of quantum metrology with a simple linear optical experiment. Contextuality is a nonclassical property known as a resource for various quantum information processing tasks. Recent studies show that contextuality by anomalous weak values can be utilized to enhance metrological precision, unraveling the role of contextuality in quantum metrology. Our contextual quantum metrology (coQM) scheme can elevate the precision inferred from the observed Fisher information as much as six times the precision limit given by the quantum Fisher information (QFI), and, when the Godambe information is used, the precision inferred becomes about two times lower than the precision limit. We achieve the contextuality-enabled precision with two mutually complementary measurements, whereas, in the conventional method, some optimal measurements to achieve the precision limit are either theoretically challenging to find or experimentally infeasible to realize. These results highlight that the contextuality of measurement selection is applicable in practice for quantum metrology.

arXiv:2311.13084•npj Quantum Information•Jul 4, 2024•2 citations

Fisher Information as a Measure of Time

B. Roy Frieden

Springer eBooks•Jan 1, 1997•6 citations

Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues

Silvana Flego, Angelo Plastino, Angel Ricardo Plastino

It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schrödinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.

arXiv:1106.2078•Journal of Modern Physics•Jan 1, 2011•3 citations

Quantum Control and Statistical Information

Maison Clouâtré

Quantum control plays a crucial role in quantum inference tasks such as parameter estimation and state discrimination. Despite this, the fields of quantum control and quantum inference have remained largely disjoint. We bridge these fields, revealing that (i) quantum control determines the fundamental performance limits of quantum estimation and state discrimination, and (ii) control of statistical information measures enables performance approaching these limits. This thesis begins by establishing an axiomatic formalization of quantum control theory and developing a mathematical framework for analyzing, approximating, and controlling the evolution of quantum systems. A self-contained treatment of optimal quantum control is presented. This treatment exploits the unique structure of quantum dynamics rather than merely borrowing notions from classical control. Quantum control systems are shown to be universally contractive, which plays an important role in the treatment of optimal quantum control and in the derivation of various approximation results. Next, the thesis proceeds by addressing statistical inference problems, with emphasis on parameter estimation and state discrimination. Controlled information measures are introduced, providing more sensible alternatives to existing information measures for quantum inference, e.g., quantum Fisher information. Controlled information measures are shown to exhibit useful properties, e.g., data-processing inequalities. Methods for deriving achievability and converse bounds on controlled information measures are developed, and adaptive control techniques for information maximization are proposed. This thesis leverages a cross-pollination of control theory, statistical inference, and quantum information towards the development of an application-focused theory of quantum inference.

•Feb 1, 2026•0 citations

Fisher information as a measure of time

B. Roy Frieden

Astrophysics and Space Science•Jan 1, 1996•8 citations
Abstract We demonstrate that the contextuality of measurement selection can enhance the precision of quantum metrology with a simple linear optical experiment. Contextuality is a nonclassical property known as a resource for various quantum information processing tasks. Recent studies show that contextuality by anomalous weak values can be utilized to enhance metrological precision, unraveling the role of contextuality in quantum metrology. Our contextual quantum metrology (coQM) scheme can elevate the precision inferred from the observed Fisher information as much as six times the precision limit given by the quantum Fisher information (QFI), and, when the Godambe information is used, the precision inferred becomes about two times lower than the precision limit. We achieve the contextuality-enabled precision with two mutually complementary measurements, whereas, in the conventional method, some optimal measurements to achieve the precision limit are either theoretically challenging to find or experimentally infeasible to realize. These results highlight that the contextuality of measurement selection is applicable in practice for quantum metrology.
It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schrödinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.
Quantum control plays a crucial role in quantum inference tasks such as parameter estimation and state discrimination. Despite this, the fields of quantum control and quantum inference have remained largely disjoint. We bridge these fields, revealing that (i) quantum control determines the fundamental performance limits of quantum estimation and state discrimination, and (ii) control of statistical information measures enables performance approaching these limits. This thesis begins by establishing an axiomatic formalization of quantum control theory and developing a mathematical framework for analyzing, approximating, and controlling the evolution of quantum systems. A self-contained treatment of optimal quantum control is presented. This treatment exploits the unique structure of quantum dynamics rather than merely borrowing notions from classical control. Quantum control systems are shown to be universally contractive, which plays an important role in the treatment of optimal quantum control and in the derivation of various approximation results. Next, the thesis proceeds by addressing statistical inference problems, with emphasis on parameter estimation and state discrimination. Controlled information measures are introduced, providing more sensible alternatives to existing information measures for quantum inference, e.g., quantum Fisher information. Controlled information measures are shown to exhibit useful properties, e.g., data-processing inequalities. Methods for deriving achievability and converse bounds on controlled information measures are developed, and adaptive control techniques for information maximization are proposed. This thesis leverages a cross-pollination of control theory, statistical inference, and quantum information towards the development of an application-focused theory of quantum inference.