Lower and upper bounds for entanglement of Rényi-α entropy

Song, Wei; Chen, Lin; Cao, Zhuo‐Liang

doi:10.1038/s41598-016-0029-9

Cited by 10 publications

(7 citation statements)

References 62 publications

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“…In the future, identification of underlying mechanisms by which cancer cells interact with ECs to promote extravasation will definitely lead to the development of new therapies to reduce metastasis. Intriguingly, recent data indicated that tumor cells implanted into the brain of nude mice spread along the abluminal surface of blood vessels instead of the bloodstream [ 182 ], which raises the possibility and likelihood of an alternative mechanism of dissemination. If other pathways besides the blood and lymphatic vessels for tumor dissemination are validated, then current therapeutics targeting cancer cells in circulation may be less effective.…”

Section: Discussionmentioning

confidence: 99%

Factors involved in cancer metastasis: a better understanding to “seed and soil” hypothesis

et al. 2017

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Metastasis has intrigued researchers for more than 100 years. Despite the development of technologies and therapeutic strategies, metastasis is still the major cause of cancer-related death until today. The famous “seed and soil” hypothesis is widely cited and accepted, and it still provides significant instructions in cancer research until today. To our knowledge, there are few reviews that comprehensively and correlatively focus on both the seed and soil factors involved in cancer metastasis; moreover, despite the fact that increasingly underlying mechanisms and concepts have been defined recently, previous perspectives are appealing but may be limited. Hence, we reviewed factors involved in cancer metastasis, including both seed and soil factors. By integrating new concepts with the classic hypothesis, we aim to provide a comprehensive understanding of the “seed and soil” hypothesis and to conceptualize the framework for understanding factors involved in cancer metastasis. Based on a dynamic overview of this field, we also discuss potential implications for future research and clinical therapeutic strategies.

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Section: Discussionmentioning

confidence: 99%

Factors involved in cancer metastasis: a better understanding to “seed and soil” hypothesis

et al. 2017

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“…Data from this study suggest that antigen-specific pTregs (but not tTregs) are liable to dysfunction in an inflammatory microenvironment, such as occurs in a high-risk host bed. This distinction between tTregs and pTregs is of critical importance, as it supports the proposition that pTregs maintain peripheral tolerance to allografts in the low-risk setting, but their function is subverted by graft site inflammation, in which case they promote rejection [118]. …”

Section: Tregs In Corneal Transplantationmentioning

confidence: 63%

“…Indeed, in an investigation of the function of tTregs and pTregs in a high-risk model of corneal transplantation, it has been demonstrated that the frequency and function of pTregs were suppressed in high-risk transplants and that this corresponded to reduced expression of IL-10 and TGF-β [118]. Data from this study suggest that antigen-specific pTregs (but not tTregs) are liable to dysfunction in an inflammatory microenvironment, such as occurs in a high-risk host bed.…”

Section: Tregs In Corneal Transplantationmentioning

confidence: 99%

Review: The function of regulatory T cells at the ocular surface

et al. 2017

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Regulatory T cells (Tregs) are critical modulators of immune homeostasis. Tregs maintain peripheral tolerance to self-antigens, thereby preventing autoimmune disease. Furthermore, Tregs suppress excessive immune responses deleterious to the host. Recent research has deepened our understanding of how Tregs function at the ocular surface. This manuscript describes the classification, the immunosuppressive mechanisms, and the phenotypic plasticity of Tregs. We review the contribution of Tregs to ocular surface autoimmune disease, as well as the function of Tregs in allergy and infection at the ocular surface. Finally, we review the role of Tregs in promoting allotolerance in corneal transplantation.

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“…A few previous attempts for entanglement upper bounds were limited to specific entanglement measures (for example, the entanglement of formation in [14] and the Rényi-α entropy in [15]). These usually cannot be extended to more complicated systems, multipartite entanglement being a key example.…”

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confidence: 99%

Estimating Lower and Upper Bounds of Entanglement

Xie¹,

Zhao²,

Zhang³

et al. 2022

Preprint

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A proper genuine multipartite entanglement (GME) measure has been found for three-qubit pure states [see Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)], but capturing useful entanglement measures for mixed states remains an open challenge. So far, it requires not only a full tomography in experiments, but also huge calculational labor. A leading proposal was made by Gühne, Reimpell, and Werner [Phys. Rev. Lett. 98, 110502 (2007)], who used expectation values of entanglement witnesses to describe a lower bound estimation of entanglement. We provide here an extension that also gives genuine upper bounds of entanglement. This advance requires only the expectation value of any Hermitian operator. Moreover, we identify a class of operators A1 which not only give good estimations, but also require a remarkably small number of experimental measurements. In this note we define our approach and illustrate it by calculating entanglement measures for a number of pure and mixed states prepared in recent experiments.

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Lower and upper bounds for entanglement of Rényi-α entropy

Cited by 10 publications

References 62 publications

Factors involved in cancer metastasis: a better understanding to “seed and soil” hypothesis

Factors involved in cancer metastasis: a better understanding to “seed and soil” hypothesis

Review: The function of regulatory T cells at the ocular surface

Estimating Lower and Upper Bounds of Entanglement

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