Generalized relative entropy (-relative entropy) is a measure of dissimilarity between two quantum states. It is a "one-shot" analogue of quantum relative entropy and shares many properties of the latter quantity. In the study of quantum information theory, we typically assume that information processing tasks are repeated multiple times, independently. The corresponding information-theoretic notions are therefore defined in the asymptotic limit. The quintessential entropy measure, von Neumann entropy, is one such notion. In contrast, the study of one-shot quantum information theory is concerned with information processing when a task is conducted only once. New entropic measures emerge in this scenario, as traditional notions cease to give a precise characterization of resource requirements. -relative entropy is one such particularly interesting measure. In the asymptotic scenario, relative entropy acts as a parent quantity for other measures besides being an important measure itself. Similarly, -relative entropy functions as a parent quantity for other measures in the one-shot scenario. (Wikipedia).
Anna Vershynina: "Quasi-relative entropy: the closest separable state & reversed Pinsker inequality"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "Quasi-relative entropy: the closest separable state and the reversed Pinsker inequality" Anna Vershynina - University of Houston Abstract: It is well known that for pure states the relative entropy of entanglement is equ
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
David Sutter: "A chain rule for the quantum relative entropy"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "A chain rule for the quantum relative entropy" David Sutter - IBM Zürich Research Laboratory Abstract: The chain rule for the conditional entropy allows us to view the conditional entropy of a large composite system as a
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
What is Relative Density? | Physics | Don't Memorise
Now that you know what Density means, it would be quite easy for you to understand what Relative Density means. Watch this video to know more. ✅To learn more about Relative Density enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&
From playlist Physics
Entropy production during free expansion of an ideal gas by Subhadip Chakraborti
Abstract: According to the second law, the entropy of an isolated system increases during its evolution from one equilibrium state to another. The free expansion of a gas, on removal of a partition in a box, is an example where we expect to see such an increase of entropy. The constructi
From playlist Seminar Series
Entropy is often taught as a measure of how disordered or how mixed up a system is, but this definition never really sat right with me. How is "disorder" defined and why is one way of arranging things any more disordered than another? It wasn't until much later in my physics career that I
From playlist Thermal Physics/Statistical Physics
(IC 3.4) Remark - an alternate proof
The non-negativity of relative entropy can also be used to show that the expected codeword length of a symbol code is bounded below by the entropy of the source. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F
From playlist Information theory and Coding
Statistics - How to make a relative frequency distribution
This video covers how to make a relative frequency distribution chart. Remember that in a relative frequency distribution we scale back the frequency using the total frequency. Depending on rounding, the total relative frequency might not be one, but should be very close. For more video
From playlist Statistics
The lecture was held within the framework of the Hausdorff Trimester Program "Dynamics: Topology and Numbers": Conference on “Transfer operators in number theory and quantum chaos” Abstract: In many classical compact settings, entropy is upper semicontinuous, i.e., given a con
From playlist Conference: Transfer operators in number theory and quantum chaos
Maxwell-Boltzmann distribution
Entropy and the Maxwell-Boltzmann velocity distribution. Also discusses why this is different than the Bose-Einstein and Fermi-Dirac energy distributions for quantum particles. My Patreon page is at https://www.patreon.com/EugeneK 00:00 Maxwell-Boltzmann distribution 02:45 Higher Temper
From playlist Physics
Optimized quantum f-divergences and data processing - M. Wilde - Main Conference - CEB T3 2017
Mark Wilde (Baton Rouge) / 11.12.2017 Title: Optimized quantum f-divergences and data processing Abstract: The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Matrix trace inequalities for quantum entropy - M. Berta - Main Conference - CEB T3 2017
Mario Berta (Imperial) / 11.12.2017 Title: Matrix trace inequalities for quantum entropy Abstract: I will present multivariate trace inequalities that extend the Golden-Thompson and Araki-Lieb-Thirring inequalities as well as some logarithmic trace inequalities to arbitrarily many matric
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Lewis Bowen - When does injectivity imply surjectivity
November 23, 2015 - Princeton University Any injective map from a finite set to itself is surjective. Ax's Theorem extends this to algebraic varieties and regular maps. Gromov invented sofic groups as a way to extend to this result to cellular automata and other settings. We'll re-prove hi
From playlist Minerva Mini Course - Lewis Bowen
(IC 3.10) Relative entropy as the mismatch inefficiency
By considering the inefficiency due to using the wrong probability distribution to design a code using Shannon coding, we arrive at the relative entropy. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F
From playlist Information theory and Coding
Roland Bauerschmidt: Lecture #1
This is a first lecture on "Log-Sobolev inequality and the renormalisation group" by Dr. Roland Bauerschmidt. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home
From playlist Summer School on PDE & Randomness
Hans Föllmer: Entropy, energy, and optimal couplings on Wiener space
HYBRID EVENT Recorded during the meeting "Advances in Stochastic Control and Optimal Stopping with Applications in Economics and Finance" the September 12, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video a
From playlist Probability and Statistics
Dominique Spehner : Measuring quantum correlations with relative Rényi entropie
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 31, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Ángela Capel: "Modified logarithmic Sobolev inequality for quantum spin systems via approximate..."
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "The modified logarithmic Sobolev inequality for quantum spin systems via approximate tensorization" Ángela Capel - Technische Universität München Abstract: Given a uniform, frustration-free family of local Lindbladians d
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
Modified Logarithmic Sobolev Inequalities: Theory... (lecture 1) by Prasad Tetali
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019