Experimentally Accessible Lower Bounds for Genuine Multipartite Entanglement and Coherence Measures

Dai, Yue; Dong, Yinmao; Xu, Zhenyu; You, Wen-Long; Zhang, Chengjie; Gühne, Otfried

doi:10.1103/physrevapplied.13.054022

Cited by 38 publications

(26 citation statements)

References 66 publications

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“…In ref. [107], the authors present a fidelity based method to derive experimentally accessible lower bounds for measures of coherence. Indeed, this can be understood as the measurement of a witness constructed as

W = false| ϕ_{\max} false| double-struck1 - false| ϕ false⟩ false⟨ ϕ false|

where

| ϕ ⟩

is any chosen pure state, and

ϕ_{\max}

denotes the coefficient of

| ϕ ⟩

with the largest magnitude in the basis

{| i ⟩}

.…”

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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W = false| ϕ_{\max} false| double-struck1 - false| ϕ false⟩ false⟨ ϕ false|

where

| ϕ ⟩

is any chosen pure state, and

ϕ_{\max}

denotes the coefficient of

| ϕ ⟩

with the largest magnitude in the basis

{| i ⟩}

.…”

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

View full text Add to dashboard Cite

show abstract

“…Besides the spectrum-estimation-based method, another two efficient coherence estimation methods for multipartite states have been proposed recently, namely the fidelitybased estimation method [44] and the witness-based estimation method [46], respectively. Specifically, C f ,C g , Cl 1 can be estimated via the fidelity-based estimation method and C R can be estimated via the witness-based estimation method.…”

Section: Comparison With Other Coherence Estimation Methodsmentioning

confidence: 99%

“…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%

“…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%

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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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“…Another one is the geometric measure of entanglement (GME) 9 , 39 , 40 . Furthermore, the expected value of entanglement witnesses can be used to estimate the GME 41 – 43 . Other different entanglement measures have been proposed for multipartite systems and mixed states 19 , 20 .…”

Section: Introductionmentioning

confidence: 99%

Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement

Zhang

Dai

Dong

et al. 2020

Sci Rep

Self Cite

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Quantifying coherence and entanglement is extremely important in quantum information processing. Here, we present numerical and analytical results for the geometric measure of coherence, and also present numerical results for the geometric measure of entanglement. on the one hand, we first provide a semidefinite algorithm to numerically calculate geometric measure of coherence for arbitrary finite-dimensional mixed states. Based on this semidefinite algorithm, we test randomly generated single-qubit states, single-qutrit states, and a special kind of d-dimensional mixed states. Moreover, we also obtain an analytical solution of geometric measure of coherence for a special kind of mixed states. on the other hand, another algorithm is proposed to calculate the geometric measure of entanglement for arbitrary two-qubit and qubit-qutrit states, and some special kinds of higher dimensional mixed states. for other states, the algorithm can get a lower bound of the geometric measure of entanglement. Randomly generated two-qubit states, the isotropic states and the Werner states are tested. furthermore, we compare our numerical results with some analytical results, which coincide with each other.

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Experimentally Accessible Lower Bounds for Genuine Multipartite Entanglement and Coherence Measures

Cited by 38 publications

References 66 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

Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement

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