Quantum Coherence Quantifiers Based on Rényi
                    <i>α</i>
                    -Relative Entropy

Shao, Lian-He; Li, Yongming; Luo, Yu; Xi, Zhengjun

doi:10.1088/0253-6102/67/6/631

Cited by 32 publications

(33 citation statements)

References 41 publications

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“…In the limit 1 a  both functions D r s a ( || ) and D q r s a ( || ) coincide with the relative entropy S r s ( || ). Coherence quantifiers of this type were studied in [28,29,44]. A related approach based on Tsallis relative entropies has also been investigated [45].…”

Section: Resource Theory Of Quantum Coherencementioning

confidence: 99%

Maximal coherence and the resource theory of purity

et al. 2018

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The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

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Section: Resource Theory Of Quantum Coherencementioning

confidence: 99%

Maximal coherence and the resource theory of purity

et al. 2018

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“…We remark that a coherence quantifier based on sandwiched Rényi relative entropy was also investigated in [6,31], but that quantifier is not a coherence measure in the sense that satisfying (C1-C4), i.e., under the BCP framework.…”

Section: Coherence Measures Based On Sandwiched Rényi Relative Enmentioning

confidence: 99%

Coherence measures based on sandwiched Rényi relative entropy*

2020

Chinese Phys. B

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Coherence is a fundamental ingredient for quantum physics and a key resource for quantum information theory. Baumgratz, Cramer, and Plenio established a rigorous framework (BCP framework) for quantifying coherence [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. In this paper, under the BCP framework we provide two classes of coherence measures based on the sandwiched Rényi relative entropy. We also prove that we can not get new coherence measures f (C(·)) by a function f acting on a given coherence measure C, except the case of qubit states.

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“…Coherence monotones of the Tsallis type were examined in [32]. Relative Rényi entropies of coherence were considered in [33,34]. In contrast to (4), these quantifiers do not reduce to a simple analytical expression.…”

Section: Preliminariesmentioning

confidence: 99%

On the role of dealing with quantum coherence in amplitude amplification

Rastegin

2018

Quantum Inf Process

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Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. As measures of coherence, the geometric coherence and the relative entropy of coherence are considered. In terms of the relative entropy of coherence, complementarity relations with the success probability seem to be the most expository. The general relations presented are illustrated within several model scenarios of amplitude amplification processes.

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Quantum Coherence Quantifiers Based on Rényi α -Relative Entropy

Cited by 32 publications

References 41 publications

Maximal coherence and the resource theory of purity

Maximal coherence and the resource theory of purity

Coherence measures based on sandwiched Rényi relative entropy*

On the role of dealing with quantum coherence in amplitude amplification

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