scholarly journals An intuitive proof of the data processing inequality

2012 ◽  
Vol 12 (5&6) ◽  
pp. 432-441
Author(s):  
Normand J. Beaudry ◽  
Renato Renner
Keyword(s):  
Data Processing ◽  
Short Proof ◽  
Relevant Information ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Fundamental Feature ◽  
Asymptotic Equipartition Property ◽  
Data Processing Inequality ◽  
Definition Of ◽  
Intuitive Proof

The data processing inequality (DPI) is a fundamental feature of information theory. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. When the smooth min-entropy is used as the relevant information measure, then the DPI follows immediately from the definition of the entropy. The DPI for the von Neumann entropy is then obtained by specializing the DPI for the smooth min-entropy by using the quantum asymptotic equipartition property (QAEP). We provide a short proof of the QAEP and therefore obtain a self-contained proof of the DPI for the von Neumann entropy.

scholarly journals WIGNER ROTATIONS, BELL STATES, AND LORENTZ INVARIANCE OF ENTANGLEMENT AND VON NEUMANN ENTROPY

2004 ◽  
Vol 02 (02) ◽  
pp. 183-200 ◽  
Author(s):  
CHOPIN SOO ◽  
CYRUS C. Y. LIN
Keyword(s):  
Lorentz Invariance ◽  
Zeta Functions ◽  
Bell States ◽  
Von Neumann Entropy ◽  
Lorentz Transformations ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Einstein Podolsky Rosen ◽  
Definition Of ◽  
Reduced Density

We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2 particles, Einstein–Podolsky–Rosen–ell entangled states and their behaviour under the Lorentz group are analyzed in the context of quantum field theory. Group theoretical considerations suggest a convenient definition of the Bell states which is slightly different from the conventional assignment. The behaviour of Bell states under arbitrary Lorentz transformations can then be described succinctly. Reduced density matrices applicable to systems of identical particles are defined through Yang's prescription. The von Neumann entropy of each of the reduced density matrix is Lorentz invariant; and its relevance as a measure of entanglement is discussed, and illustrated with an explicit example. A regularization of the entropy in terms of generalized zeta functions is also suggested.

RELATIVE VON NEUMANN ENTROPY FOR EVALUATING AMINO ACID CONSERVATION

2010 ◽  
Vol 08 (05) ◽  
pp. 809-823 ◽  
Author(s):  
FREDRIK JOHANSSON ◽  
HIROYUKI TOH
Keyword(s):  
Amino Acid ◽  
Sequence Analysis ◽  
Shannon Entropy ◽  
Von Neumann Entropy ◽  
Sequence Alignments ◽  
Multiple Sequence ◽  
Von Neumann ◽  
Multiple Sequence Alignments ◽  
Previous Definition ◽  
Definition Of

The Shannon entropy is a common way of measuring conservation of sites in multiple sequence alignments, and has also been extended with the relative Shannon entropy to account for background frequencies. The von Neumann entropy is another extension of the Shannon entropy, adapted from quantum mechanics in order to account for amino acid similarities. However, there is yet no relative von Neumann entropy defined for sequence analysis. We introduce a new definition of the von Neumann entropy for use in sequence analysis, which we found to perform better than the previous definition. We also introduce the relative von Neumann entropy and a way of parametrizing this in order to obtain the Shannon entropy, the relative Shannon entropy and the von Neumann entropy at special parameter values. We performed an exhaustive search of this parameter space and found better predictions of catalytic sites compared to any of the previously used entropies.

scholarly journals Switching and Swapping of Quantum Information: Entropy and Entanglement Level

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 717
Author(s):  
Marek Sawerwain ◽  
Joanna Wiśniewska ◽  
Roman Gielerak
Keyword(s):  
Quantum Information ◽  
Quantum Systems ◽  
Von Neumann Entropy ◽  
Crucial Issue ◽  
Schmidt Decomposition ◽  
Intrinsic Decoherence ◽  
Von Neumann ◽  
Local Quantum ◽  
Definition Of ◽  
Moriya Interaction

Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementary properties analysed through the prism of the concept of the entropy, are presented. As an example of the local information swapping usage, we demonstrate a certain realisation of the quantum switch. Entanglement levels, during the work of the switch, are calculated with the Negativity measure and a separability criterion based on the von Neumann entropy, spectral decomposition and Schmidt decomposition. Results of numerical experiments, during which the entanglement levels are estimated for systems under consideration with and without distortions, are presented. The noise is generated by the Dzyaloshinskii-Moriya interaction and the intrinsic decoherence is modelled by the Milburn equation. This work contains a switch realisation in a circuit form—built out of elementary quantum gates, and a scheme of the circuit which estimates levels of entanglement during the switch’s operating.

scholarly journals Quantum Features of Macroscopic Fields: Entropy and Dynamics

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 705
Author(s):  
Robert Alicki
Keyword(s):  
Wave Equations ◽  
Particle Density ◽  
Von Neumann Entropy ◽  
Quantum Field ◽  
Von Neumann ◽  
Single Particle Density ◽  
Definition Of ◽  
Thermal Sources ◽  
Reduced State ◽  
State Of The Field

Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics.

scholarly journals ENTANGLEMENT IN VALENCE-BOND-SOLID STATES

2010 ◽  
Vol 24 (11) ◽  
pp. 1361-1440 ◽  
Author(s):  
VLADIMIR E. KOREPIN ◽  
YING XU
Keyword(s):  
Density Matrix ◽  
Condensed Matter ◽  
Valence Bond ◽  
Von Neumann Entropy ◽  
Information Measurement ◽  
Von Neumann ◽  
Solid States ◽  
The Subject ◽  
Definition Of ◽  
Valence Bond Solid

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review, we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Rényi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.

scholarly journals Entropy Accumulation

2020 ◽  
Vol 379 (3) ◽  
pp. 867-913 ◽  
Author(s):  
Frédéric Dupuis ◽  
Omar Fawzi ◽  
Renato Renner
Keyword(s):  
Large System ◽  
Von Neumann Entropy ◽  
Independence Assumption ◽  
Total Uncertainty ◽  
Von Neumann ◽  
First Order ◽  
Asymptotic Equipartition Property ◽  
The Individual

Abstract We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an n-partite system $$A = (A_1, \ldots A_n)$$ A = ( A 1 , … A n ) corresponds to the sum of the entropies of its parts $$A_i$$ A i . The Asymptotic Equipartition Property implies that this is indeed the case to first order in n—under the assumption that the parts $$A_i$$ A i are identical and independent of each other. Here we show that entropy accumulation occurs more generally, i.e., without an independence assumption, provided one quantifies the uncertainty about the individual systems $$A_i$$ A i by the von Neumann entropy of suitably chosen conditional states. The analysis of a large system can hence be reduced to the study of its parts. This is relevant for applications. In device-independent cryptography, for instance, the approach yields essentially optimal security bounds valid for general attacks, as shown by Arnon-Friedman et al. (SIAM J Comput 48(1):181–225, 2019).

scholarly journals Entanglement entropy between virtual and real excitations in quantum electrodynamics

2018 ◽  
Vol 33 (13) ◽  
pp. 1850081 ◽  
Author(s):  
Juan Sebastián Ardenghi
Keyword(s):  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Perturbation Expansion ◽  
Inner Product ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Virtual Particles ◽  
Quantum Operators ◽  
Definition Of

The aim of this work is to introduce the entanglement entropy of real and virtual excitations of fermion and photon fields. By rewriting the generating functional of quantum electrodynamics theory as an inner product between quantum operators, it is possible to obtain quantum density operators representing the propagation of real and virtual particles. These operators are partial traces, where the degrees of freedom traced out are unobserved excitations. Then the von Neumann definition of entropy can be applied to these quantum operators and in particular, for the partial traces taken over by the internal or external degrees of freedom. A universal behavior is obtained for the entanglement entropy for different quantum fields at zeroth order in the coupling constant. In order to obtain numerical results at different orders in the perturbation expansion, the Bloch–Nordsieck model is considered, where it is shown that for some particular values of the electric charge, the von Neumann entropy increases or decreases with respect to the noninteracting case.

scholarly journals Sustainability and Stakeholder Awareness: A Case Study of a Scottish University

2021 ◽  
Vol 13 (8) ◽  
pp. 4186
Author(s):  
Abdulhakeem Raji ◽  
Abeer Hassan
Keyword(s):  
Signaling Theory ◽  
Relevant Information ◽  
Voluntary Exercise ◽  
Communication Tool ◽  
Individual Interviews ◽  
Study Approach ◽  
Research Findings ◽  
Definition Of ◽  
The University

This paper adopted a case study approach to investigate the sustainability practices of a Scottish university in order to understand if sustainability forms part of its central policy agenda. As such, the paper focuses on the levels of awareness and disclosure of their sustainable practices, measuring the impacts and effectiveness of those initiatives. This paper introduces signaling theory to explore the idea that appropriate communication via integrated thinking can close the gap between the organization and its stakeholders. We believe that the provision of this relevant information will lead to better communication between the organization and its stakeholders, supporting a signaling theory interpretation. Therefore, we are suggesting that integrated thinking is an internal process that organizations can follow to increase the level of disclosure as a communication tool with stakeholders. From the literature reviewed, four themes were identified (definition of university sustainability, sustainability awareness, disclosure framework within universities, and level of accountability). The research adopted a pragmatic view and conducted individual interviews with participants belonging to three stakeholder groups (members of the university’s senior management, the governing council, and the student union executive). Although this study focused on just one Scottish university, it should still provide some insight for the better understanding of the underpinning issues surrounding the sustainability accountability practices of Scottish universities in general. The research findings indicated that the university prioritized only two sustainability dimensions—economic and environmental—and that the university still perceived sustainability as a voluntary exercise. Additionally, it is evident that the university had no framework in place for measuring its sustainability delivery—and therefore had no established medium of communicating these activities to its stakeholders. Moreover, research findings showed that the social and educational context of sustainability was lacking at the university. The university has done little or nothing to educate its stakeholders on sustainability.

scholarly journals Quaternion Processing Techniques for Color Synthesized NDT Thermography

2021 ◽  
Vol 11 (2) ◽  
pp. 790
Author(s):  
Pablo Venegas ◽  
Rubén Usamentiaga ◽  
Juan Perán ◽  
Idurre Sáez de Ocáriz
Keyword(s):  
Signal To Noise Ratio ◽  
High Capacity ◽  
Synthetic Data ◽  
Relevant Information ◽  
Color Images ◽  
Destructive Testing ◽  
Application Procedure ◽  
Definition Of ◽  
Characterization Procedure ◽  
Processing Techniques

Infrared thermography is a widely used technology that has been successfully applied to many and varied applications. These applications include the use as a non-destructive testing tool to assess the integrity state of materials. The current level of development of this application is high and its effectiveness is widely verified. There are application protocols and methodologies that have demonstrated a high capacity to extract relevant information from the captured thermal signals and guarantee the detection of anomalies in the inspected materials. However, there is still room for improvement in certain aspects, such as the increase of the detection capacity and the definition of a detailed characterization procedure of indications, that must be investigated further to reduce uncertainties and optimize this technology. In this work, an innovative thermographic data analysis methodology is proposed that extracts a greater amount of information from the recorded sequences by applying advanced processing techniques to the results. The extracted information is synthesized into three channels that may be represented through real color images and processed by quaternion algebra techniques to improve the detection level and facilitate the classification of defects. To validate the proposed methodology, synthetic data and actual experimental sequences have been analyzed. Seven different definitions of signal-to-noise ratio (SNR) have been used to assess the increment in the detection capacity, and a generalized application procedure has been proposed to extend their use to color images. The results verify the capacity of this methodology, showing significant increments in the SNR compared to conventional processing techniques in thermographic NDT.

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