PPT-New Results of Quantum-proof Randomness

Extractors Xiaodi Wu MIT 1 st Trustworthy Quantum Information Workshop Ann Arbor USA 1 b ased on work w KaiMin Chung and Xin Li arXiv 14112315 and work wKaiMin Chung . . 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. is Exponentially Stronger than . Classical Communication. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. Bo’az. . Klartag. Tel Aviv University. 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 . and quantum adversaries. AmnonTa-Shma. Tel-Aviv University. Is randomness a feasible resource?. Probabilistic algorithms assume access to truly uniform bits. . Cryptography assumes one can generate truly random bits. Fernando . G.S.L. . Brand. ão. ETH Zürich. W. ith . B. Barak . (. MSR). ,. . M. . Christandl. . (ETH),. . A. Harrow . (MIT), . J. . Kelner. . (MIT), . D. . Steurer. . (Cornell), . J. Yard . (Station Q), . Upper and Lower Bounds. Matthew . Coudron. , Thomas . Vidick. , Henry Yuen. arXiv:1305.6626. The motivating question. Is it possible to test randomness?. The motivating question. Is it possible to test randomness?. 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. Aram Harrow (MIT). Simons Institute 2014.1.17. a theorem. Let M. 2. R. +. m. £. n. .. Say that a set S. ⊆[n]. k. is δ-good if . ∃φ:[m]. k. .  S. such that ∀(j. 1,. …, j. k. )∈S, . f(k,δ):= max{ |S| : ∃S⊆[n]. Fernando . G.S.L. . Brand. ão. ETH Zürich. Based on joint work with M. . Christandl. and J. Yard. Journees. . Deferation. de . Reserche. en . Mathematiques. de Paris Centre/GT . Informatique. . Days. , November 2011. , . Murcia, . Spain. Antonio . Acín. ICREA . Professor. at ICFO-. Institut. de . Ciencies. . Fotoniques. , Barcelona. Device-Independent Quantum . Information Processing. Computational security. Fernando . G.S.L. . Brand. ão. University College London. New Perspectives on . Thermalization. , Aspen 2014. p. artially based on joint work with . Aram Harrow . and . Michal . Horodecki. Plan. 1. . Aram Harrow (MIT). Simons Institute 2014.1.17. a theorem. Let M. 2. R. . m. £. n. .. Say that a set S. ⊆[n]. k. is δ-good if . ∃φ:[m]. k. .  S. such that ∀(j. 1,. …, j. k. )∈S, . f(k,δ):= max{ |S| : ∃S⊆[n]. Xiaodi Wu. University of Oregon. 1. Yaoyun. Shi. . University of Michigan. Kai-. Min Chung. Academia . Sinica. 2. Right Time for Quantum Information Theorists to . . Jump Into Black-holes. 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.