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. AS if for every trajectory we have as implies is the unique equilibrium point system is locally asymptotically stable LAS near or at if there is an R st 0 k as Basic Lyapunov theory 122 brPage 3br often we change coordinates so that 0 ie we use a 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. Convergence & Divergence Theorems. Convergence & Divergence Theorems. Convergence & Divergence Theorems. Convergence & Divergence Theorems. 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 . Dung Nguyen. Chicago 19. th. January. Content. Motivation . Quantum bit (qubit) vs Classical bit (bit). Quantum Computation . Quantum Communication. Conclusion. Motivation. The end of Moore’s law scaling in silicon (because of quantum effects of particle at scale smaller than 7nm).. 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. . C. S. Unnikrishnan. Fundamental Interactions Laboratory. Tata Institute of Fundamental Research,. Mumbai 400005. tifr.res.in/~filab. Resolution of nonlocality puzzle in EPR paradox, . C. S. Unnikrishnan, Current Science, . 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. . 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 . -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 . 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 . Part 1. Outline. Introduction. Problems of classical physics. Black-body Radiation. experimental observations. Wien’s displacement law. Stefan – Boltzmann law. Rayleigh - Jeans. Wien’s radiation law.