other seminars:

:: Fri 10/2, 2:10pm in MSR, Horace Mann Conference Room, One Memorial Drive (note different place and time) Ryan O'Donnell (CMU) In quantum mechanics, the state rho of a ddimensional particle is given by a d x d PSD matrix of trace 1. The "quantum tomography problem" is to estimate rho accurately using as few "copies" of the state as possible. The special case of "quantum spectrum estimation" involves just estimating the eigenvalues alpha_1, ..., alpha_d of rho, which form a probability distribution. By virtue of some representation theory, understanding these problems mostly boils down to understanding certain statistics of random words with i.i.d. letters drawn from the alpha_i distribution. These statistics involve longest increasing subsequences, and more generally, the shape of Young tableaus produced by the RobinsonSchenstedKnuth algorithm. In this talk we will discuss new probabilistic, combinatorial, and representationtheoretic tools for these problems, and the consequent new upper and lower bounds for quantum tomography. This is joint work with John Wright Barry Sanders (University of Calgary) Quantum information processing is possible via multichannel linear (passive) interferometry with photon number states as some or all of the inputs and photoncoincidence detection at the output ports. The KnillLaflammeMilburn nonlinear sign gate on dualrail photonic qubits and the AaronsonArkhipov BosonSampling scheme are salient examples of linear photonic quantum information processing. Implementations of quantum walks also make use of linear photon interferometry. The famous HongOuMandel dip presents the heart of what makes linear photon interferometry quantum and furthermore serves as an indispensable characterization tool for sources and interferometers. Our aim is to advance linear photonic quantum interferometry to serve as a precise and accurate tool for optical quantum information processing. To this end we develop and experimentally test a theory for accurate and precise characterization of the HongOuMandel dip setup, extend this theory for accurate and precise characterization of multichannel interferometry based on photon coincidences, extend the HongOuMandel dip concept beyond twochannel to multichannel interferometry, develop theory and (classical) algorithms for computing irreducible representations of SU(m) whose elements represent all mchannel interferometers, and determine the effects of extraneous multiphoton contributions to the desired outputs. Our approach allows for nonsimultaneous photon arrival times, which removes the typical symmetrization assumption in photon interferometry and leads to photon coincidence rates depending on immanants of SU(m) matrices or submatrices; immanants generalize the concepts of permanents and determinants to allow for partial symmetries. For linear photon interferometry to move beyond the proofofprinciple stage to solving computational problems, they need to be reliable, accurate and precise within known error. Furthermore their performance needs to be benchmarked against the best classical simulation algorithms. Our results are enabling the field to advance in this direction. :: Fri 10/23, 1:30pm in 6C442 Michael Walter (Stanford) TBA :: Fri 10/30, 1:30pm in 6C442 Ashley Montanaro (U. Bristol) TBA Beni Yoshida (Caltech) TBA :: Fri 11/13, 1:30pm in 6C442 Ke Li (IBM/MIT) TBA :: Fri 11/20, 1:30pm in 6C442 David Gosset (Caltech) TBA 