Detecting coherence via spectrum estimation

Yu, Xiao-Dong; Gühne, Otfried

doi:10.1103/physreva.99.062310

Cited by 27 publications

(25 citation statements)

References 73 publications

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“…For such systems, a spectrum‐based estimation method was proposed in ref. [116] which can be used to provide bounds for coherence measures such as the robustness of coherence

C_{R}

, the relative entropy of coherence

C_{r}

, or the ℓ 1 ‐norm of coherence

C_{ℓ_{1}}

. The crucial aspect of this scheme is that a small number of local measurements can suffice to provide useful bounds.…”

Section: Experimental Progress On the Resource Theory Of Quantum Coherencementioning

confidence: 99%

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

Streltsov

Regula

et al. 2021

Adv Quantum Tech

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Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence can be extracted and used for quantum technological applications. In this work, the progress of this research is reviewed, focusing in particular on recent experimental efforts. After a brief review of the underlying theory, the main platforms for realizing the experiments are discussed: linear optics, nuclear magnetic resonance, and superconducting systems. Experimental detection and quantification of coherence, experimental state conversion and coherence distillation, and experiments investigating the dynamics of quantum coherence are then considered. Experiments exploring the connections between coherence and uncertainty relations, path information, and coherence of operations and measurements are also reviewed. Experimental efforts on multipartite and multilevel coherence are also discussed.

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“…For such systems, a spectrum‐based estimation method was proposed in ref. [116] which can be used to provide bounds for coherence measures such as the robustness of coherence

C_{R}

, the relative entropy of coherence

C_{r}

, or the ℓ 1 ‐norm of coherence

C_{ℓ_{1}}

. The crucial aspect of this scheme is that a small number of local measurements can suffice to provide useful bounds.…”

Section: Experimental Progress On the Resource Theory Of Quantum Coherencementioning

confidence: 99%

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

Streltsov

Regula

et al. 2021

Adv Quantum Tech

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“…Efficient protocols for detecting quantum coherence without quantum state tomography have been recently investigated [38][39][40][41][42][43][44][45][46]. However, the initial proposals require either complicated experimental settings for multipartite quantum systems [38][39][40] or complex numerical optimizations [41].…”

Section: Introductionmentioning

confidence: 99%

“…However, the initial proposals require either complicated experimental settings for multipartite quantum systems [38][39][40] or complex numerical optimizations [41]. An experiment-friendly tool, the so-called spectrum-estimationbased method, requires local measurements and simple post-processing [42], and has been experimentally demonstrated to measure the relative entropy of coherence [43]. Other experiment-friendly tools, such as the fidelity-based estimation method [44] and the witness-based estimation method [46], have been successively proposed very recently.…”

Section: Introductionmentioning

confidence: 99%

“…Still, there are several unexplored matters along this line of research. First, on the theoretical side, although it has been studied that the spectrum-estimation-based method is capable of detecting the coherence of several coherence measures [42], there still exists some coherence measures that are unexplored. On the experimental side, the realization is focused on the detection of relative entropy of coherence [43], and its feasibility for other coherence measures has not been tested.…”

Section: Introductionmentioning

confidence: 99%

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The Tightness of Multipartite Coherence from Spectrum Estimation

Ding

Fang

2021

Entropy

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Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, the l1-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation.

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“…Before doing that, we stress that the lattice theoretical aspects of majorization theory have not been sufficiently exploited in comparison with other features of it in the area of quantum information. Indeed, the first applications were given in [30,31]; only recently, new applications of the majorization lattice have been found [32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Optimal common resource in majorization-based resource theories

et al. 2019

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We address the problem of finding the optimal common resource for an arbitrary family of target states in quantum resource theories based on majorization, that is, theories whose conversion law between resources is determined by a majorization relationship, such as it happens with entanglement, coherence or purity. We provide a conclusive answer to this problem by appealing to the completeness property of the majorization lattice. We give a proof of this property that relies heavily on the more geometric construction provided by the Lorenz curves, which allows to explicitly obtain the corresponding infimum and supremum. Our framework includes the case of possibly nondenumerable sets of target states (i.e. targets sets described by continuous parameters). In addition, we show that a notion of approximate majorization, which has recently found application in quantum thermodynamics, is in close relation with the completeness of this lattice. Finally, we provide some examples of optimal common resources within the resource theory of quantum coherence.

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Detecting coherence via spectrum estimation

Cited by 27 publications

References 73 publications

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

The Tightness of Multipartite Coherence from Spectrum Estimation

Optimal common resource in majorization-based resource theories

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