PPT-Robust Randomness Expansion

Upper and Lower Bounds Matthew Coudron Thomas Vidick Henry Yuen arXiv13056626 The motivating question Is it possible to test randomness The motivating question Is it possible to test randomness. The original motivation for extractors was to simulate randomized algorithms with weak random sources as might arise in nature This motivation is still compelling but extractors have taken on a much wider signi64257cance in the years since they were Both Sides of the Coin. Dave Mark – Intrinsic Algorithm LLC. Brian Schwab – Blizzard. Dave Mark. President & Lead Designer . of . Intrinsic . Algorithm . LLC. Independent Game Studio. AI Consulting Company. . device. independent . randomness. . amplification. with . few. devices. F.G.S.L Brandao. 1. , R. . . Ramanathan. 2. . A. Grudka. 3. , K.. 4. , M.. 5. ,P.. 6. Horodeccy. 1. Department . of Computer Science, University College London. the . Classical World. Kai-Min Chung . Academia . Sinica. , Taiwan. 1. Based on joint works with . Xin. Li, . Yaoyun. Shi, and . Xiaodi. Wu. Original Motivation from . 9. 0’s. Randomness is . extremely useful . Follow-Up:. Further into Python. Part 3: . Random. Numbers. Part 3: . “Random”. Numbers. Part 3: . Pseudo. -Random. Numbers. Why Random Numbers?. Traditional use: cryptography. http://www.diablotin.com/librairie/networking/puis/figs/puis_0604.gif. Lior . Eldar. MIT . / . CTP. Joint work with Aram Harrow. Highlights. We prove a conjecture of Freedman and Hastings [‘12] that there exist quantum systems of “robust entanglement”- called NLTS.. minimal. assumptions. needed for. infinite. randomness . expansion?. Henry Yuen . (MIT). Stellenbosch, South Africa. 27 October 2015. 0. 1. 1. 0. 1. 1. 0. 1. 0. 1. 0. 0. 1. 1. 1. 0. 1. 0. 1. 1. 1. 0. Shachar. Lovett (IAS). Coding, Complexity and . Sparsity. workshop. August 2011. Overview. Pseudo-randomness – what? why?. Concrete examples. Local independence. Expander graphs. Small space computations. and Patterns of Illusion. GROUP 1. Celestine. Walter. Jun Yue (Presenter). OUTLINE. Illusions – human perception. Causes. Effects. Randomness in the financial market. Hot-hand fallacy. Bill Miller. Matt . Coudron. and Henry Yuen. 6.845. 12/12/12. God does not play dice. . . --. Albert Einstein. Einstein, stop telling God what to do. . . --. Niels. Bohr. The Motivating Question. Is it possible to test randomness?. Randomness. ？. 隨機是指缺乏模式及可預測性的. 事件. e.g.. . 擲骰、六合彩、粒子運動等. 甚麼是機率. Probability. ？. 機率是用以描述隨機事件結果的數學. With gratitude to the John Templeton Foundation who supported this project but is not responsible for its content. . “… if purpose is part of this universe, then randomness, by definition, is not possible. This is also one of the rationales for religious opposition to evolution, where, according to theory, (non-random) selection is applied to the results of random genetic variation.” . Feb 18. th. , 2014. IQI Seminar, Caltech. Kai-Min Chung. . IIS, . Sinica,Taiwan. Yaoyun. Shi. . University of Michigan. Xiaodi Wu. . MIT/UC Berkeley. device. …….. Ext(. x,s. i. ). Ext(x,0). Decouple. Lovett (IAS). Coding, Complexity and . Sparsity. workshop. August 2011. Overview. Pseudo-randomness – what? why?. Concrete examples. Local independence. Expander graphs. Small space computations.