PPT-Quantum de Finetti theorems under local measurements

Aram Harrow MIT QIP 2013 based on arXiv12106367 joint work with Fernando Brandão ETH Symmetric States is permutation symmetric in the B subsystems if for every permutation π. Does Bell’s theorem prevent the use of causal explanations in quantum mechanics?. Part I:. Locality, Bell’s version of locality, and its discontents. The greatest mystery in science?. Locality. = “things do not go faster than . Fernando . G.S.L. . Brand. ão. ETH Zürich. Based on joint work with . A. Harrow . and . M. . Horodecki. . Quo Vadis Quantum Physics, Natal 2013. Quantum is Hard. Use of DoE supercomputers by area . Challenges and Opportunities. Fernando . G.S.L. . Brand. ão. Universidade. Federal de Minas . Gerais. , Brazil. Based on joint work with. M. . Christandl. , A. Harrow, M. . Horodecki. , J. Yard. PI, 02/11/2011. Fang Song. IQC, University of Waterloo. -- “Quantum-Friendly” Reductions. 2. How do . quantum . attacks change classical cryptography?. Crypto-systems based on the hardness of factoring and discrete-log are . Fernando Brandão (UCL). Aram Harrow (MIT). arXiv:1210.6367. methods to analyze. SDP hierarchies. motivation/warmup. nonlinear optimization --> convex optimization. D(n) = conv {xx. T. : x∈S. n. Groundstates. Fernando . G.S.L. . Brand. ão. Imperial -> UCL. Based on joint work with . A. Harrow . . Paris, April 2013. Quantum Many-Body Systems. Quantum Hamiltonian . Byron Smith. December 11, 2013. What is Quantum State Tomography?. What is Bayesian Statistics?. Conditional Probabilities. Bayes. ’ Rule. Frequentist. vs. Bayesian. Example: . Schrodinger’s Cat. 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. . . Theorems. m. example. Write a proof.. Given. : . Prove. : . . Statements Reason. . 1.. ___________________ _______________________. . 2.. ___________________ _______________________. . 3.. ___________________ _______________________. Algebra. Huntington’s Postulates. Truth Tables. Graphic Symbols. Boolean Algebra Theorems. 1. Boolean . Algebra. 2. Boolean . Algebra. A fire sprinkler system should spray water if high heat is sensed and the system is set to . -Polygon. : a closed plane figure with at least 3 sides that are segments that only intersect at their endpoints where no adjacent sides are collinear. -Regular Polygon. : . a polygon that is both equilateral and . Aram Harrow. . based on joint work with . Fernando G.S.L. Brandão. (ETHZ->Imperial). PCP theorem. Classical k-CSPs:. Given constraints . C={C. i. }. , choose an assignment . σ. mapping . n. variables to an alphabet . ). www.drfrostmaths.com. . Last modified: . 31. st. August 2015. RECAP. : Parts of a Circle. Sector. (Minor). Segment. Diameter. Radius. Tangent. Chord. (Minor) Arc. Circumference. ?. ?. ?. ?. ?. !. Fernando Brandão (UCL). Aram Harrow (MIT). arXiv:. 1310.0017. Constraint Satisfaction Problems. x. 1. c. 1. c. 2. c. 3. k. -CSP:. Variables . {x. 1. , …, . x. n. } in . Σ. n. . Alphabet . Σ. Constraints .