Articles containing proofs | Theorems in quantum mechanics | Quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James Park, in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist (the same result would be independently derived in 1982 by Wootters and Zurek as well as Dieks the same year). The aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors. For example, one might use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits without violating the no-cloning theorem as no well-defined state may be defined in terms of a subsystem of an entangled state. The no-cloning theorem (as generally understood) concerns only pure states whereas the generalized statement regarding mixed states is known as the no-broadcast theorem. The no-cloning theorem has a time-reversed dual, the no-deleting theorem. Together, these underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger compact category. This formulation, known as categorical quantum mechanics, allows, in turn, a connection to be made from quantum mechanics to linear logic as the logic of quantum information theory (in the same sense that intuitionistic logic arises from Cartesian closed categories). (Wikipedia).
Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91
There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point
From playlist Math Foundations
Brill-Noether part 4: Noether's Theorem
From playlist Brill-Noether
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Real numbers and Cauchy sequences of rationals(I) | Real numbers and limits Math Foundations 111
We introduce the idea of a `Cauchy sequence of rational numbers'. The notion is in fact logically problematic. It involves epsilons and N's, much as does the notion of a limit, and suffers from similiar issues: how to guarantee that we can find an infinite number of N's for an infinite num
From playlist Math Foundations
Duality Theorem In this video, I use a neat little trick to show that the limit as n goes to infinity of 2^n is infinity, by using the fact (shown before) that the limit of (1/2)^n is 0. Exponential Limit: https://youtu.be/qxlSclbmh-w Other examples of limits can be seen in the playlis
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Why You Should Never Say "It's Just A Theory"
A portion of our culture distrusts the scientific method, assuming that there are transcendent truths unknowable by science. But nothing is truly out of bounds for science. If it's real, it can be studied, and tested. Perhaps the greatest misunderstanding our culture has about the scientif
From playlist Science for Common Folk
No-Cloning Theorem (Proof) | No-Broadcast Theorem | Quantum Mechanics
We present and prove the no-cloning theorem in #QuantumMechanics and mention the no-broadcast theorem, which is a generalization of the no-cloning theorem. For further information on the no-cloning theorem, we can recommend the book „Introduction to Quantum Mechanics“ by Griffiths, espec
From playlist Quantum Mechanics, Quantum Field Theory
Support MinutePhysics on Patreon: http://www.patreon.com/minutephysics Three Blue One Brown: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw Why you can’t clone Schrödinger’s cat: this video presents the full proof of the “No Cloning” Theorem in Quantum Mechanics – without any f
From playlist MinutePhysics
Lecture 5 | Quantum Entanglements, Part 1 (Stanford)
Lecture 5 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 1, Fall 2006). Recorded October 23, 2006 at Stanford University. This Stanford Continuing Studies course is the first of a three-quarter sequence of classes exploring the "quantum entanglements" in moder
From playlist Course | Quantum Entanglements: Part 1 (Fall 2006)
An Infinite Product Conjecture - Monday Math Nugget #2
Today we're answering a question posed in the comment section of the previous MMN... The conjecture is: since any quotient of finite products of integers cannot be an integer if all factors in the numerator are odd and at least one in the denominator is even, then a quotient of infinite
From playlist Monday Math Nuggets
Celestial Amplitudes and Asymptotic Symmetries (Lecture 2) by Stephan Stieberger
PROGRAM RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online
From playlist Recent Developments in S-matrix Theory (Online)
The Limit Does NOT Exist (Limit Example 4)
Epsilon Definition of a Limit In this video, I illustrate the epsilon-N definition of a limit by showing that the limit of (-1)^n as n goes to infinity does NOT exist. The method I present is more generally useful to show that a limit does not exist. Other examples of limits can be seen
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Anne Broadbent - Information-Theoretic Quantum Cryptography Part 1 of 2 - IPAM at UCLA
Recorded 27 July 2022. Anne Broadbent of the University of Ottawa presents "Information-Theoretic Quantum Cryptography" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: These lectures are an introduction to the interplay between quantum information and cryp
From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography
Quantum computation (Lecture 02) by Peter Young
ORGANIZERS : Abhishek Dhar and Sanjib Sabhapandit DATE : 27 June 2018 to 13 July 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the ninth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics
From playlist Bangalore School on Statistical Physics - IX (2018)
Complete Statistical Theory of Learning (Vladimir Vapnik) | MIT Deep Learning Series
Lecture by Vladimir Vapnik in January 2020, part of the MIT Deep Learning Lecture Series. Slides: http://bit.ly/2ORVofC Associated podcast conversation: https://www.youtube.com/watch?v=bQa7hpUpMzM Series website: https://deeplearning.mit.edu Playlist: http://bit.ly/deep-learning-playlist
From playlist AI talks
The Detectability Lemma and Quantum Gap Amplification - Itai Arad
Itai Arad Hebrew University of Jerusalem October 5, 2009 Constraint Satisfaction Problems appear everywhere. The study of their quantum analogues (in which the constraints no longer commute), has become a lively area of study, and various recent results provide interesting insights into q
From playlist Mathematics
Here's a re-enactment of the famous paradox known as the "infinite monkey theorem."
From playlist Cosmic Journeys
Ethereum Smart Contracts Tutorial | Deploying Smart Contracts | Blockchain Training | Edureka
( Blockchain Training : https://www.edureka.co/blockchain-tra... ) This Edureka Ethereum Smart Contracts Tutorial (Ethereum blog: https://goo.gl/9vFwJj ) video will give you a complete understanding on Ethereum and Smart Contracts. This video helps you to learn following topics: 1. Why is
From playlist Blockchain Tutorial Videos | Edureka
What the HECK is Time?! (in Einstein’s Relativity)
In special and general relativity, we imagine time as just another dimension of space in something called "spacetime." Unfortunately, this picture leads to questions about determinism and free will. Is that really how it works? What does the concept of spacetime actually say about the univ
From playlist Gravity as Spacetime Curvature
Set Theory (Part 20): The Complex Numbers are Uncountably Infinite
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will establish a bijection between the complex numbers and the real numbers, showing that the complex numbers are also uncountably infinite. This will eventually mean that the cardinal
From playlist Set Theory by Mathoma