Fidelity and trace-norm distances for quantifying coherence

Shao, Lian-He; Xi, Zhengjun; Fan, Heng; Li, Yongming

doi:10.1103/physreva.91.042120

Cited by 284 publications

(235 citation statements)

References 18 publications

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“…It is worth pointing out that the coherence measures induced by l 2 norm and the fidelity do not constitute valid coherence monotones, since for both quantities the strong monotonicity (2) does not hold in general [9,14]. Moreover, though the trace-norm measure of coherence was proved to be a strong monotone for all qubit and X states, a recent work showed that the trace norm of coherence cannot be regarded as a legitimate coherence measure for general states [15].…”

Section: Defining the Problemmentioning

confidence: 99%

Maximal coherence in a generic basis

Yao

Dong

et al. 2016

Phys. Rev. A

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Since quantum coherence is an undoubted characteristic trait of quantum physics, the quantification and application of quantum coherence has been one of the long-standing central topics in quantum information science. Within the framework of a resource theory of quantum coherence proposed recently, a fiducial basis should be pre-selected for characterizing the quantum coherence in specific circumstances, namely, the quantum coherence is a basis-dependent quantity. Therefore, a natural question is raised: what are the maximum and minimum coherences contained in a certain quantum state with respect to a generic basis? While the minimum case is trivial, it is not so intuitive to verify in which basis the quantum coherence is maximal. Based on the coherence measure of relative entropy, we indicate the particular basis in which the quantum coherence is maximal for a given state, where the Fourier matrix (or more generally, complex Hadamard matrices) plays a critical role in determining the basis. Intriguingly, though we can prove that the basis associated with the Fourier matrix is a stationary point for optimizing the l 1 norm of coherence, numerical simulation shows that it is not a global optimal choice.

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Section: Defining the Problemmentioning

confidence: 99%

Maximal coherence in a generic basis

Yao

Dong

et al. 2016

Phys. Rev. A

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“…It has been shown that the promising fidelity of coherence does not in general satisfy (C2b) under the subselection of the measurement condition [9]. Generally, the bosonic single mode Hilbert space H is spanned by an uncountable basis {|n } ∞ n=0 called the Fock (number state) basis.…”

mentioning

confidence: 99%

Quantifying coherence in infinite-dimensional systems

et al. 2016

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We study the quantification of coherence in infinite dimensional systems, especially the infinite dimensional bosonic systems in Fock space. We show that given the energy constraints, the relative entropy of coherence serves as a well-defined quantification of coherence in infinite dimensional systems. Via using the relative entropy of coherence, we also generalize the problem to multi-mode Fock space and special examples are considered. It is shown that with a finite average particle number, increasing the number of modes of light can enhance the relative entropy of coherence. With the mean energy constraint, our results can also be extended to other infinite-dimensional systems.Quantum coherence arising from quantum superposition principle is a fundamental aspect of quantum physics [1]. The laser [2] and superfluidity [3] are examples of quantum coherence, whose effects are evident at the macroscopic scale. However, the framework of quantification of coherence has only been methodically investigated recently. The first attempt to address the classification of quantum coherence as physical resources by T. Baumgratz et. al., who have established a rigorous framework for the quantification of coherence based on distance measures in finite dimensional setting [4]. With such a fundational framework for coherence, one can find the appropriate distance measures to quantify coherence in a fixed basis by measuring the distance between the quantum stateρ and its nearest incoherent state. After the framework for coherence has been proposed, it receives increasing attentions. Up to now, all the results for quantifying the quantum coherence are assumed the finite dimensional setting, which is neither necessary nor desirable. In consideration of the relevant physical situations such as quantum optics states of light, it must require further investigations on infinite dimensional systems.In this paper, we aim to investigate the quantification of coherence in infinite dimensional systems. Specificly, we focus on the infinite dimensional bosonic systems in Fock space [10] which are used to describe the most notable quantum optics states of light [11] and Gaussian states [12][13][14]. We show that when considering the energy constraints, the relative en- * Electronic address: liyongm@snnu.edu.cn † Electronic address: hfan@iphy.ac.cn tropy of coherence serves as a well-defined quantification of coherence in infinite dimensional systems and the l 1 norm of coherence fails. Via using the relative entropy of coherence, we also generalize the results to multi-mode Fock space and special examples are considered. It is shown that with a finite average particle number, increasing the number of modes of light can enhance the relative entropy of coherence. Our results can also be extended to other infinite-dimensional systems with energy constraints. Our work investigates special and experimentally relevant cases and the most general and easy to use quantifiers, which is significant and essential in quantum physics as well as quantum opt...

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“…Furthermore, a geometric measure of coherence is also proposed [15,18,19] which is a full coherence monotone [18]. The geometric measure is given by C g (ρ) = 1 − max σ∈I F(ρ, σ), where I is the set of all incoherent states and…”

Section: A Quantum Coherencementioning

confidence: 99%

“…Moreover, combined with the tensor product structure of quantum state space, it gives rise to the novel concepts such as entanglement and quantum correlations. It, being the premise of quantum correlations in multipartite systems, has attracted the attention of quantum information community significantly, and * asukumar@hri.res.in in addition to its quantification [17][18][19], other developments like the freezing phenomena [20], the coherence transformations under incoherent operations [21], establishment of geometric lower bound for a coherence measure [22], the complementarity between coherence and mixedness [23], its relation with other measures of quantum correlations and creation of coherence using unitary operations [24,25], erasure of quantum coherence [26], and catalytic transformations of coherence [27] have been reported recently.…”

Section: Introductionmentioning

confidence: 99%

Quantum coherence: Reciprocity and distribution

Kumar

2017

Physics Letters A

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Quantum coherence is the outcome of the superposition principle. Recently, it has been theorized as a quantum resource, and is the premise of quantum correlations in multipartite systems. It is therefore interesting to study the coherence content and its distribution in a multipartite quantum system. In this work, we show analytically as well as numerically the reciprocity between coherence and mixedness of a quantum state. We find that this trade-off is a general feature in the sense that it is true for large spectra of measures of coherence and of mixedness. We also study the distribution of coherence in multipartite systems by looking at monogamytype relation-which we refer to as additivity relation-between coherences of different parts of the system. We show that for the Dicke states, while the normalized measures of coherence violate the additivity relation, the unnormalized ones satisfy the same.

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Fidelity and trace-norm distances for quantifying coherence

Cited by 284 publications

References 18 publications

Maximal coherence in a generic basis

Maximal coherence in a generic basis

Quantifying coherence in infinite-dimensional systems

Quantum coherence: Reciprocity and distribution

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