In quantum information, the diamond norm, also known as completely bounded trace norm, is a norm on the space of quantum operations, or more generally on any linear map that acts on complex matrices. Its main application is to measure the "single use distinguishability" of two quantum channels. If an agent is randomly given one of two quantum channels, permitted to pass one state through the unknown channel, and then measures the state in an attempt to determine which operation they were given, then their maximal probability of success is determined by the diamond norm of the difference of the two channels. Although the diamond norm can be efficiently computed via semidefinite programming, it is in general difficult to obtain analytical expressions and those are known only for a few particular cases. (Wikipedia).
13C Norm and Distance in Euclidean n Space
Norm and distance in Euclidean n-Space.
From playlist Linear Algebra
Matrix Norms : Data Science Basics
What does it mean to take the norm of a matrix? Vector Norms Video: https://www.youtube.com/watch?v=5fN2J8wYnfw Eigenvalues and Eigenvectors Video: https://www.youtube.com/watch?v=glaiP222JWA
From playlist Data Science Basics
1A Introduction to this course on limits
A course on limits in calculus for healthcare and life sciences students.
From playlist Life Science Math: Limits in calculus
From playlist Linear Algebra Ch 6
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
David Gross: Diamond norm as improved regularizer for low rank matrix recovery
David Gross: Diamond norm as improved regularizer for low rank matrix recovery Abstract: In the common approach to low-rank matrix recovery, one uses the nuclear norm as a convex surrogate for rank. Geometric proof techniques like Tropp's Bowling scheme or Mendelson's small ball method bo
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
Beata Randrianantoanina: On a difference between two methods of low-distortion embeddings of...
Abstract: In a recent paper, the speaker and M.I. Ostrovskii developed a new metric embedding method based on the theory of equal-signs-additive (ESA) sequences developed by Brunel and Sucheston in 1970’s. This method was used to construct bilipschitz embeddings of diamond and Laakso graph
From playlist Analysis and its Applications
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From playlist Statistical Regression
Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
Linear regression (6): Regularization
Lp regularization penalties; comparing L2 vs L1
From playlist cs273a
Here we explore why the L1 norm promotes sparsity in optimization problems. This is an incredibly important concept in machine learning, and data science more broadly, as sparsity helps us to improve robustness and prevent overfitting. Book Website: http://databookuw.com Book PDF: ht
From playlist Sparsity and Compression [Data-Driven Science and Engineering]
Every Distance in Data Science (Almost 100K Subs!)
0:00 Intro 2:19 Euclidean Distance 5:47 Manhattan Distance 9:14 Minkowski Distance 12:49 Chebyshev Distance 15:40 Cosine Distance 19:35 Hamming Distance 20:17 Haversine Distance Lasso Regression : https://www.youtube.com/watch?v=jbwSCwoT51M Curse of Dimensionality : https://www.youtube.c
From playlist Data Science Basics
Asymptotic properties of random quantum states and channels - Z.Puchała - Workshop 2 - CEB T3 2017
Zbigniew Puchała / 21.10.17 Asymptotic properties of random quantum states and channels Properties of random mixed states of dimension N distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large N, due to the concentration of measure pheno
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Lecture 8: Norms of Vectors and Matrices
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k A norm is a way to
From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Introduction to FPP (Lecture 2) by Jack Thomas Hanson,
PROGRAM : FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS : Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE : 11 July 2022 to 29 July 2022 VENUE : Ramanujan Lecture Hall and online T
From playlist First-Passage Percolation and Related Models 2022 Edited
My Patreon : https://www.patreon.com/user?u=49277905
From playlist Statistical Regression
Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture - 04) by Misha Kapovich
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017