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:1711.10110

Comment on "Quantifying quantum coherence with quantum Fisher information"

Hyukjoon Kwon, Kok Chuan Tan, Seongjeon Choi, Hyunseok Jeong

Published Nov 28, 2017• 0 citations
arXivHTMLPDF

Abstract

We show that contrary to the claim in Sci. Rep. 7, 15492 (2017), the quantum Fisher information itself is not a valid coherence measure based on the resource theory of coherence because it can increase via an incoherent operation.
DOI
10.48550/arxiv.1711.10110

Related papers

Quantum Fisher information on its own is not a valid measure of the coherence

Hyukjoon Kwon, Kok Chuan Tan, Seongjeon Choi +1 more

We show that contrary to the claim in Feng and Wei (2017), the quantum Fisher information itself is not a valid measure of the coherence based on the resource theory because it can increase via an incoherent operation.

Results in Physics•May 7, 2018•9 citations

Quantifying quantum coherence with quantum Fisher information

X. N. Feng, L. F. Wei

Quantum coherence is one of the old but always important concepts in quantum mechanics, and now it has been regarded as a necessary resource for quantum information processing and quantum metrology. However, the question of how to quantify the quantum coherence has just been paid the attention recently (see, e.g., Baumgratz et al. PRL, 113. 140401 (2014)). In this paper we verify that the well-known quantum Fisher information (QFI) can be utilized to quantify the quantum coherence, as it satisfies the monotonicity under the typical incoherent operations and the convexity under the mixing of the quantum states. Differing from most of the pure axiomatic methods, quantifying quantum coherence by QFI could be experimentally testable, as the bound of the QFI is practically measurable. The validity of our proposal is specifically demonstrated with the typical phase-damping and depolarizing evolution processes of a generic single-qubit state, and also by comparing it with the other quantifying methods proposed previously.

Scientific Reports•Nov 8, 2017•39 citations

Quantifying coherence with respect to general measurements via quantum Fisher information

Jianwei Xu

The standard quantum coherence theory is defined with respect to an orthonormal basis of a Hilbert space. Recently, Bischof, Kampermann and Bru% ß generalized the notion of coherence into the case of general measurements, and also, they established a rigorous resource theory of coherence with respect to general measurements. In this paper, we propose such a coherence measure with respect to general measurements via quantum Fisher information, and provide an application of this measure.

arXiv:2107.10615•Jul 22, 2021•0 citations

Comment on “Quantum coherence measures based on Fisher information with applications”

Jianwei Xu

In their recent paper [Li et al., Phys. Rev. A 103, 012401 (2021)], the authors proposed two quantities ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})$ in Eq. (11) and ${C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ in Eq. (12). The authors proved that ${C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ is a valid coherence measure in Theorem 5 and proved that ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})={C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ in Proposition 4. In this Comment, we show that the proof of Proposition 4 is not justified, that is, ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})={C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ is not true, in general. Consequently, whether ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})$ is a valid coherence measure is still an open problem.

Physical Review A•May 10, 2022•0 citations

Quantum coherence versus quantum uncertainty

Shunlong Luo, Yuan Sun

The notion of measurement is of both foundational and instrumental significance in quantum mechanics, and coherence destroyed by measurements (decoherence) lies at the very heart of quantum to classical transition. Qualitative aspects of this spirit have been widely recognized and analyzed ever since the inception of quantum theory. However, axiomatic and quantitative investigations of coherence are attracting great interest only recently with several figures of merit for coherence introduced [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. While these resource theoretic approaches have many appealing and intuitive features, they rely crucially on various notions of incoherent operations which are sophisticated, subtle, and not uniquely defined, as have been critically assessed [Chitambar and Gour, Phys. Rev. Lett. 117, 030401 (2016)]. In this paper, we elaborate on the idea that coherence and quantum uncertainty are dual viewpoints of the same quantum substrate, and address coherence quantification by identifying coherence of a state (with respect to a measurement) with quantum uncertainty of a measurement (with respect to a state). Consequently, coherence measures may be set into correspondence with measures of quantum uncertainty. In particular, we take average quantum Fisher information as a measure of quantum uncertainty, and introduce the corresponding measure of coherence, which is demonstrated to exhibit desirable properties. Implications for interpreting quantum purity as maximal coherence, and quantum discord as minimal coherence, are illustrated.

Physical Review A•Aug 25, 2017•140 citations

Quantum Fisher Information with Coherence

Hradil, Z., Řeháček, J., Sánchez-Soto, L. +1 more

In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.

•Nov 14, 2019•44 citations
Quantum coherence is one of the old but always important concepts in quantum mechanics, and now it has been regarded as a necessary resource for quantum information processing and quantum metrology. However, the question of how to quantify the quantum coherence has just been paid the attention recently (see, e.g., Baumgratz et al. PRL, 113. 140401 (2014)). In this paper we verify that the well-known quantum Fisher information (QFI) can be utilized to quantify the quantum coherence, as it satisfies the monotonicity under the typical incoherent operations and the convexity under the mixing of the quantum states. Differing from most of the pure axiomatic methods, quantifying quantum coherence by QFI could be experimentally testable, as the bound of the QFI is practically measurable. The validity of our proposal is specifically demonstrated with the typical phase-damping and depolarizing evolution processes of a generic single-qubit state, and also by comparing it with the other quantifying methods proposed previously.
In their recent paper [Li et al., Phys. Rev. A 103, 012401 (2021)], the authors proposed two quantities ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})$ in Eq. (11) and ${C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ in Eq. (12). The authors proved that ${C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ is a valid coherence measure in Theorem 5 and proved that ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})={C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ in Proposition 4. In this Comment, we show that the proof of Proposition 4 is not justified, that is, ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})={C}_{\mathrm{F}}^{C}(\ensuremath{\rho}|\mathcal{K})$ is not true, in general. Consequently, whether ${C}_{\mathrm{F}}^{D}(\ensuremath{\rho}|\mathcal{K})$ is a valid coherence measure is still an open problem.
The notion of measurement is of both foundational and instrumental significance in quantum mechanics, and coherence destroyed by measurements (decoherence) lies at the very heart of quantum to classical transition. Qualitative aspects of this spirit have been widely recognized and analyzed ever since the inception of quantum theory. However, axiomatic and quantitative investigations of coherence are attracting great interest only recently with several figures of merit for coherence introduced [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. While these resource theoretic approaches have many appealing and intuitive features, they rely crucially on various notions of incoherent operations which are sophisticated, subtle, and not uniquely defined, as have been critically assessed [Chitambar and Gour, Phys. Rev. Lett. 117, 030401 (2016)]. In this paper, we elaborate on the idea that coherence and quantum uncertainty are dual viewpoints of the same quantum substrate, and address coherence quantification by identifying coherence of a state (with respect to a measurement) with quantum uncertainty of a measurement (with respect to a state). Consequently, coherence measures may be set into correspondence with measures of quantum uncertainty. In particular, we take average quantum Fisher information as a measure of quantum uncertainty, and introduce the corresponding measure of coherence, which is demonstrated to exhibit desirable properties. Implications for interpreting quantum purity as maximal coherence, and quantum discord as minimal coherence, are illustrated.
In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.