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

Science

Making a measure of quantum coherence

Ian S. Osborne

Published Oct 30, 2014• 0 citations
Publisher

Abstract

Quantum Physics The notion that particles have properties of waves lies at the heart of quantum mechanics. When quantum systems interact, their interaction can be described in terms of interfering waves, whose coherence is of utmost importance in working out how these waves ultimately interfere. Determining how much coherence there is in a system or how much is required for a particular process is difficult to quantify, though. Baumgratz et al. present a rigorous mathematical framework for the quantification of coherence and identify intuitive and easily computable measures that can be used to compute it. They argue that having such a quantifiable metric will have important implications for describing energy transfer processes or transferring quantum information between quantum elements. Phys. Rev. Lett. 10.1103/PhysRevLett.113.140401 (2014).

DOI
10.1126/science.346.6209.597-d

Related papers

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

Quantifying coherence of Gaussian states

Jianwei Xu

Coherence arises from the superposition principle and plays a key role in quantum mechanics. Recently, Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)] established a rigorous framework for quantifying the coherence of finite-dimensional quantum states. In this work we provide a framework for quantifying the coherence of Gaussian states and explicitly give a coherence measure for Gaussian states based on the relative entropy.

arXiv:1510.02916•Physical Review A•Mar 7, 2016•125 citations

Interferometric visibility and coherence

Tanmoy Biswas, María García Díaz, Andreas Winter

Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.

arXiv:1701.05051•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Jul 1, 2017•78 citations

Quantifying Coherence

Tillmann Baumgratz, M. Cramer, Martin Bodo Plenio

We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining conditions for measures of coherence we identify classes of functionals that satisfy these conditions and other, at first glance natural quantities, that do not qualify as coherence measures. We conclude with an outline of the questions that remain to be answered to complete the theory of coherence as a resource.

arXiv:1311.0275•Physical Review Letters•Sep 29, 2014•2,751 citations

Superposition Quantification*

Li-Na 利娜 Chang 常, Shunlong Luo, Yuan Sun

Abstract The principle of superposition is universal and lies at the heart of quantum theory. Although ever since the inception of quantum mechanics a century ago, superposition has occupied a central and pivotal place, rigorous and systematic studies of the quantification issue have attracted significant interests only in recent years, and many related problems remain to be investigated. In this work we introduce a figure of merit which quantifies superposition from an intuitive and direct perspective, investigate its fundamental properties, connect it to some coherence measures, illustrate it through several examples, and apply it to analyze wave-particle duality.

Communications in Theoretical Physics•Nov 1, 2017•24 citations

Quantifying Interference via Coherence

Yuan Sun, Shunlong Luo

Abstract Interference, which has its origin in the superposition principle, is one of the hallmarks of wave mechanics and constitutes a versatile resource for many information processing tasks. As such, it is actually a manifestation of coherence. Despite its long history in the development of physics, quantitative studies of interference are still an important topic. Traditionally, interference is often characterized via the fringe visibility from an operational perspective. This is experimentally convenient. However, from a theoretic perspective, it is desirable to reveal information‐theoretic aspects of interference. In this work, coherence of a state (with respect to a unitary operator parameterized by the interfering paths and phase shifts in multi‐path interference) is first quantified in terms of a generalized version of the Wigner‐Yanase skew information, two natural quantifiers of interference are then introduced via this coherence measure. Basic properties of these quantifiers of interference are further revealed, and the concepts are illustrated through several examples.

Annalen der Physik•Oct 8, 2021•15 citations
Quantum Physics
The notion that particles have properties of waves lies at the heart of quantum mechanics. When quantum systems interact, their interaction can be described in terms of interfering waves, whose coherence is of utmost importance in working out how these waves ultimately interfere. Determining how much coherence there is in a system or how much is required for a particular process is difficult to quantify, though. Baumgratz et al. present a rigorous mathematical framework for the quantification of coherence and identify intuitive and easily computable measures that can be used to compute it. They argue that having such a quantifiable metric will have important implications for describing energy transfer processes or transferring quantum information between quantum elements.
Phys. Rev. Lett. 10.1103/PhysRevLett.113.140401 (2014).
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.
Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.
We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining conditions for measures of coherence we identify classes of functionals that satisfy these conditions and other, at first glance natural quantities, that do not qualify as coherence measures. We conclude with an outline of the questions that remain to be answered to complete the theory of coherence as a resource.
Abstract The principle of superposition is universal and lies at the heart of quantum theory. Although ever since the inception of quantum mechanics a century ago, superposition has occupied a central and pivotal place, rigorous and systematic studies of the quantification issue have attracted significant interests only in recent years, and many related problems remain to be investigated. In this work we introduce a figure of merit which quantifies superposition from an intuitive and direct perspective, investigate its fundamental properties, connect it to some coherence measures, illustrate it through several examples, and apply it to analyze wave-particle duality.
Abstract Interference, which has its origin in the superposition principle, is one of the hallmarks of wave mechanics and constitutes a versatile resource for many information processing tasks. As such, it is actually a manifestation of coherence. Despite its long history in the development of physics, quantitative studies of interference are still an important topic. Traditionally, interference is often characterized via the fringe visibility from an operational perspective. This is experimentally convenient. However, from a theoretic perspective, it is desirable to reveal information‐theoretic aspects of interference. In this work, coherence of a state (with respect to a unitary operator parameterized by the interfering paths and phase shifts in multi‐path interference) is first quantified in terms of a generalized version of the Wigner‐Yanase skew information, two natural quantifiers of interference are then introduced via this coherence measure. Basic properties of these quantifiers of interference are further revealed, and the concepts are illustrated through several examples.