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Entropy
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Entropic Uncertainty Relations and Their Applications
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Entropic Uncertainty Relations and Their Applications

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (30 November 2019) | Viewed by 19450

Special Issue Editor

Prof. Dr. Wonmin Son

E-Mail Website1 Website2
Guest Editor
Department of Physics, Sogang University, Seoul 04107, Republic of Korea
Interests: quantum foundation, information and entanglement; generalised Bell’s inequality and non-locality; entropic uncertainty relation; many-body quantum systems

Special Issue Information

Dear Colleagues

It is well-known that the uncertainty principle is at the very heart of quantum theory, and it provides the clear distinction from an ordinary classical picture on the understanding of our nature. Through the later development of its quantification, it has been known that the scope of quantum uncertainty has been extended further using the notion of entropy, and it has been understood that the richer structure of quantum state characterization using entropy is also possible to be further unveiled. Additionally, recent development in information theoretic approaches on the various quantum states is also strongly motivating us to inspect the structural details of the quantum states through the new windows—entropic uncertainty relation. In this regard, we believe that there are a vast number of new challenges in the direction of investigation still remaining, and there is much of interest to be revealed through the characterization of the unknown. We would like to open this to your valuable contribution.

Prof. Dr. Wonmin Son
Guest Editor

Manuscript Submission Information

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Keywords

  • entropic uncertainty relation
  • quantum entanglement
  • quantum information
  • quantum foundations
  • probabilistic theories
  • quantum computation
  • quantum communications

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Published Papers (5 papers)

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Research

14 pages, 1165 KiB  
Article
Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
by Kyunghyun Baek, Hyunchul Nha and Wonmin Son
Entropy 2019, 21(3), 270; https://doi.org/10.3390/e21030270 - 11 Mar 2019
Cited by 5 | Viewed by 3131
Abstract
We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches [...] Read more.
We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Życzkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Życzkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen–Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables. Full article
(This article belongs to the Special Issue Entropic Uncertainty Relations and Their Applications)
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19 pages, 878 KiB  
Article
Limiting Uncertainty Relations in Laser-Based Measurements of Position and Velocity Due to Quantum Shot Noise
by Andreas Fischer
Entropy 2019, 21(3), 264; https://doi.org/10.3390/e21030264 - 8 Mar 2019
Cited by 10 | Viewed by 3677
Abstract
With the ongoing progress of optoelectronic components, laser-based measurement systems allow measurements of position as well as displacement, strain and velocity with unbeatable speed and low measurement uncertainty. The performance limit is often studied for a single measurement setup, but a fundamental comparison [...] Read more.
With the ongoing progress of optoelectronic components, laser-based measurement systems allow measurements of position as well as displacement, strain and velocity with unbeatable speed and low measurement uncertainty. The performance limit is often studied for a single measurement setup, but a fundamental comparison of different measurement principles with respect to the ultimate limit due to quantum shot noise is rare. For this purpose, the Cramér-Rao bound is described as a universal information theoretic tool to calculate the minimal achievable measurement uncertainty for different measurement techniques, and a review of the respective lower bounds for laser-based measurements of position, displacement, strain and velocity at particles and surfaces is presented. As a result, the calculated Cramér-Rao bounds of different measurement principles have similar forms for each measurand including an indirect proportionality with respect to the number of photons and, in case of the position measurement for instance, the wave number squared. Furthermore, an uncertainty principle between the position uncertainty and the wave vector uncertainty was identified, i.e., the measurement uncertainty is minimized by maximizing the wave vector uncertainty. Additionally, physically complementary measurement approaches such as interferometry and time-of-flight positions measurements as well as time-of-flight and Doppler particle velocity measurements are shown to attain the same fundamental limit. Since most of the laser-based measurements perform similar with respect to the quantum shot noise, the realized measurement systems behave differently only due to the available optoelectronic components for the concrete measurement task. Full article
(This article belongs to the Special Issue Entropic Uncertainty Relations and Their Applications)
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18 pages, 328 KiB  
Article
A Survey of the Concept of Disturbance in Quantum Mechanics
by Ernesto Benítez Rodríguez and Luis Manuel Arévalo Aguilar
Entropy 2019, 21(2), 142; https://doi.org/10.3390/e21020142 - 2 Feb 2019
Cited by 11 | Viewed by 3168
Abstract
The concept of disturbance is of transcendental importance in Quantum Mechanics (QM). This key concept has been described in two different ways, the first one considering that the disturbance affects observables like x and p, as in the Heisenberg’s analysis of the [...] Read more.
The concept of disturbance is of transcendental importance in Quantum Mechanics (QM). This key concept has been described in two different ways, the first one considering that the disturbance affects observables like x and p, as in the Heisenberg’s analysis of the measurement process and the other one takes into consideration that disturbance affects the state of the system instead. Entropic information measures have provided a path for studying disturbance in these both approaches; in fact, we found that initially it was studied by employing these entropic measures. In addition, in the last decade, there was an extensive amount of analyses and several new definitions of the disturbance concept emerged. Many crucial factors like this have inspired this concise paper which gathers the different concepts and definitions that have emerged through time for the better understanding of this topic. Full article
(This article belongs to the Special Issue Entropic Uncertainty Relations and Their Applications)
15 pages, 626 KiB  
Article
Efficient High-Dimensional Quantum Key Distribution with Hybrid Encoding
by Yonggi Jo, Hee Su Park, Seung-Woo Lee and Wonmin Son
Entropy 2019, 21(1), 80; https://doi.org/10.3390/e21010080 - 17 Jan 2019
Cited by 10 | Viewed by 5152
Abstract
We propose a schematic setup of quantum key distribution (QKD) with an improved secret key rate based on high-dimensional quantum states. Two degrees-of-freedom of a single photon, orbital angular momentum modes, and multi-path modes, are used to encode secret key information. Its practical [...] Read more.
We propose a schematic setup of quantum key distribution (QKD) with an improved secret key rate based on high-dimensional quantum states. Two degrees-of-freedom of a single photon, orbital angular momentum modes, and multi-path modes, are used to encode secret key information. Its practical implementation consists of optical elements that are within the reach of current technologies such as a multiport interferometer. We show that the proposed feasible protocol has improved the secret key rate with much sophistication compared to the previous 2-dimensional protocol known as the detector-device-independent QKD. Full article
(This article belongs to the Special Issue Entropic Uncertainty Relations and Their Applications)
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13 pages, 300 KiB  
Article
Einstein-Podolsky-Rosen Steering Inequalities and Applications
by Ying Yang and Huaixin Cao
Entropy 2018, 20(9), 683; https://doi.org/10.3390/e20090683 - 7 Sep 2018
Cited by 8 | Viewed by 3560
Abstract
Einstein-Podolsky-Rosen (EPR) steering is very important quantum correlation of a composite quantum system. It is an intermediate type of nonlocal correlation between entanglement and Bell nonlocality. In this paper, based on introducing definitions and characterizations of EPR steering, some EPR steering inequalities are [...] Read more.
Einstein-Podolsky-Rosen (EPR) steering is very important quantum correlation of a composite quantum system. It is an intermediate type of nonlocal correlation between entanglement and Bell nonlocality. In this paper, based on introducing definitions and characterizations of EPR steering, some EPR steering inequalities are derived. With these inequalities, the steerability of the maximally entangled state is checked and some conditions for the steerability of the X -states are obtained. Full article
(This article belongs to the Special Issue Entropic Uncertainty Relations and Their Applications)
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