Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

Baek, Kyunghyun; Nha, Hyunchul; Son, Wonmin

doi:10.3390/e21030270

Cited by 6 publications

(5 citation statements)

References 47 publications

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“…Entropic PURs in quantum theory can be derived also by means of majorization [122,123,124,125,126,127]. This method of majorization can be also applied to GPTs.…”

Section: Remark 39mentioning

confidence: 99%

Convexity and uncertainty in operational quantum foundations

Takakura¹

2022

Preprint

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List of papersThis thesis is based on the following papers:1. (Reproduced from [1], with the permission of AIP Publishing) Ryo Takakura, Takayuki Miyadera, "Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories", Journal of Mathematical Physics, 61, 082203 (2020); 2. ([2]) Ryo Takakura, Takayuki Miyadera, "Entropic uncertainty relations in a class of generalized probabilistic theories", Journal of Physics A: Mathematical and Theoretical, 54, 315302 (2021); 3. ([3]) Teiko Heinosaari, Takayuki Miyadera, Ryo Takakura, "Testing incompatibility of quantum devices with few states", Physical Review A, 104, 032228 (2021); 4. ([4]) Ryo Takakura, "Entropy of mixing exists only for classical and quantumlike theories among the regular polygon theories",

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“…Entropic PURs in quantum theory can be derived also by means of majorization [122,123,124,125,126,127]. This method of majorization can be also applied to GPTs.…”

Section: Remark 39mentioning

confidence: 99%

Convexity and uncertainty in operational quantum foundations

Takakura¹

2022

Preprint

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“…Remark 3.1.1. Entropic PURs in quantum theory can be derived also by means of majorization [51][52][53][54][55][56]. This method of majorization can be also applied to GPTs.…”

Section: Entropic Pursmentioning

confidence: 99%

Entropic uncertainty relations in a class of generalized probabilistic theories

Takakura¹,

Miyadera²

2021

J. Phys. A: Math. Theor.

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Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar to the quantum one by Buscemi et al (2014 Phys. Rev. Lett. 112 050401) are proved in those theories. These results manifest that the entropic structure in the uncertainty relations is not restricted to quantum theory and therefore is universal one. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated.

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“…In this sense, we say that the Rényi entropy is deemed as a generalization of Shannon entropy. Based on Rényi entropy, for generalized positive‐operator‐valued measure (POVM) measurements, the uncertainty relation is derived by utilizing a direct‐sum majorization relation . In addition, Maassen and Uffink have shown that Equation could be generalzied to more general case by using the Rényi entropies.…”

Section: Uncertainty Relation In the Absence Of A Quantum Memorymentioning

confidence: 99%

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

Wang

Ming

et al. 2019

Annalen der Physik

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Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy-based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum-memory-assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.

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Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

Cited by 6 publications

References 47 publications

Convexity and uncertainty in operational quantum foundations

Convexity and uncertainty in operational quantum foundations

Entropic uncertainty relations in a class of generalized probabilistic theories

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

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